How to find out if a point is on a line with an equation - PSAT Math

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Question

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

Answer

The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:

2_x_ - 3(1) = 5

2_x_ - 3 = 5

2_x_ = 8

x = 4. So the missing x-value on line l is 4.

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Question

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

Answer

Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.

2(x) + 9(7) = 71

2x + 63 = 71

2x = 8

x = 4

Therefore the answer is (4, 7)

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Question

$\dpi{100} \small 5x+25y = 125$

Which point lies on this line?

Answer

$\dpi{100} \small 5x+25y = 125$

Test the coordinates to find the ordered pair that makes the equation of the line true:

$\dpi{100} \small (5,4)$

$\dpi{100} \small 5 (5) + 25 (4) = 25 + 100 = 125$

$\dpi{100} \small (1,5)$

$\dpi{100} \small 5(1)+25(5)= 5+125=130$

$\dpi{100} \small (5,1)$

$\dpi{100} \small 5(5)+25(1)= 25+25=50$

$\dpi{100} \small (5,5)$

$\dpi{100} \small 5(5)+25(5)= 25+125=150$

$\dpi{100} \small (1,4)$

$\dpi{100} \small 5(1)+25(4)= 5+100=105$

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Question

Which of the following lines contains the point (8, 9)?

Answer

In order to find out which of these lines is correct, we simply plug in the values $\dpi{100} \small x=8$ and $\dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\dpi{100} \small 3x-6=2y$

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Question

Points D and E lie on the same line and have the coordinates $\left ( 1,2\right )$ and $\left ( 5,7\right )$ , respectively. Which of the following points lies on the same line as points D and E?

Answer

The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation

$slope = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

$slope = \frac{7-2}{5-1} = \frac{5}{4}$

Therefore, you can get an equation in the line in point-slope form, which is

.

Plug in the answer options, and you will find that only the point $\left ( 3,4.5\right )$ solves the equation.

Compare your answer with the correct one above

Question

Which of the following points is on the line given by the equation $y=\frac{1}{2}x+3$ ?

Answer

In order to solve this, try each of the answer choices in the equation:

$y=\frac{1}{2}x+3$

For example, when we try (3,4), we find:

$4=\frac{1}{2}(3)+3$

This does not work. When we try all the choices, we find that only (2,4) works:

$y=\frac{1}{2}x+3$

$4=\frac{1}{2}(2)+3$

Compare your answer with the correct one above

Question

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

Answer

The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:

2_x_ - 3(1) = 5

2_x_ - 3 = 5

2_x_ = 8

x = 4. So the missing x-value on line l is 4.

Compare your answer with the correct one above

Question

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

Answer

Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.

2(x) + 9(7) = 71

2x + 63 = 71

2x = 8

x = 4

Therefore the answer is (4, 7)

Compare your answer with the correct one above

Question

$\dpi{100} \small 5x+25y = 125$

Which point lies on this line?

Answer

$\dpi{100} \small 5x+25y = 125$

Test the coordinates to find the ordered pair that makes the equation of the line true:

$\dpi{100} \small (5,4)$

$\dpi{100} \small 5 (5) + 25 (4) = 25 + 100 = 125$

$\dpi{100} \small (1,5)$

$\dpi{100} \small 5(1)+25(5)= 5+125=130$

$\dpi{100} \small (5,1)$

$\dpi{100} \small 5(5)+25(1)= 25+25=50$

$\dpi{100} \small (5,5)$

$\dpi{100} \small 5(5)+25(5)= 25+125=150$

$\dpi{100} \small (1,4)$

$\dpi{100} \small 5(1)+25(4)= 5+100=105$

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Question

Which of the following lines contains the point (8, 9)?

Answer

In order to find out which of these lines is correct, we simply plug in the values $\dpi{100} \small x=8$ and $\dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\dpi{100} \small 3x-6=2y$

Compare your answer with the correct one above

Question

Points D and E lie on the same line and have the coordinates $\left ( 1,2\right )$ and $\left ( 5,7\right )$ , respectively. Which of the following points lies on the same line as points D and E?

Answer

The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation

$slope = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

$slope = \frac{7-2}{5-1} = \frac{5}{4}$

Therefore, you can get an equation in the line in point-slope form, which is

.

Plug in the answer options, and you will find that only the point $\left ( 3,4.5\right )$ solves the equation.

Compare your answer with the correct one above

Question

Which of the following points is on the line given by the equation $y=\frac{1}{2}x+3$ ?

Answer

In order to solve this, try each of the answer choices in the equation:

$y=\frac{1}{2}x+3$

For example, when we try (3,4), we find:

$4=\frac{1}{2}(3)+3$

This does not work. When we try all the choices, we find that only (2,4) works:

$y=\frac{1}{2}x+3$

$4=\frac{1}{2}(2)+3$

Compare your answer with the correct one above

Question

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

Answer

The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:

2_x_ - 3(1) = 5

2_x_ - 3 = 5

2_x_ = 8

x = 4. So the missing x-value on line l is 4.

Compare your answer with the correct one above

Question

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

Answer

Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.

2(x) + 9(7) = 71

2x + 63 = 71

2x = 8

x = 4

Therefore the answer is (4, 7)

Compare your answer with the correct one above

Question

$\dpi{100} \small 5x+25y = 125$

Which point lies on this line?

Answer

$\dpi{100} \small 5x+25y = 125$

Test the coordinates to find the ordered pair that makes the equation of the line true:

$\dpi{100} \small (5,4)$

$\dpi{100} \small 5 (5) + 25 (4) = 25 + 100 = 125$

$\dpi{100} \small (1,5)$

$\dpi{100} \small 5(1)+25(5)= 5+125=130$

$\dpi{100} \small (5,1)$

$\dpi{100} \small 5(5)+25(1)= 25+25=50$

$\dpi{100} \small (5,5)$

$\dpi{100} \small 5(5)+25(5)= 25+125=150$

$\dpi{100} \small (1,4)$

$\dpi{100} \small 5(1)+25(4)= 5+100=105$

Compare your answer with the correct one above

Question

Which of the following lines contains the point (8, 9)?

Answer

In order to find out which of these lines is correct, we simply plug in the values $\dpi{100} \small x=8$ and $\dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\dpi{100} \small 3x-6=2y$

Compare your answer with the correct one above

Question

Points D and E lie on the same line and have the coordinates $\left ( 1,2\right )$ and $\left ( 5,7\right )$ , respectively. Which of the following points lies on the same line as points D and E?

Answer

The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation

$slope = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

$slope = \frac{7-2}{5-1} = \frac{5}{4}$

Therefore, you can get an equation in the line in point-slope form, which is

.

Plug in the answer options, and you will find that only the point $\left ( 3,4.5\right )$ solves the equation.

Compare your answer with the correct one above

Question

Which of the following points is on the line given by the equation $y=\frac{1}{2}x+3$ ?

Answer

In order to solve this, try each of the answer choices in the equation:

$y=\frac{1}{2}x+3$

For example, when we try (3,4), we find:

$4=\frac{1}{2}(3)+3$

This does not work. When we try all the choices, we find that only (2,4) works:

$y=\frac{1}{2}x+3$

$4=\frac{1}{2}(2)+3$

Compare your answer with the correct one above

Question

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

Answer

The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:

2_x_ - 3(1) = 5

2_x_ - 3 = 5

2_x_ = 8

x = 4. So the missing x-value on line l is 4.

Compare your answer with the correct one above

Question

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

Answer

Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.

2(x) + 9(7) = 71

2x + 63 = 71

2x = 8

x = 4

Therefore the answer is (4, 7)

Compare your answer with the correct one above

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How to find out if a point is on a line with an equation - PSAT Math

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

The equation of a line is: 2x + 9y = 71 Which of these points is on that line?

Which point lies on this line?

Test the coordinates to find the ordered pair that makes the equation of the line true:

Which of the following lines contains the point (8, 9)?

In order to find out which of these lines is correct, we simply plug in the values and into each equation and see if it balances. The only one for which this will work is

Points D and E lie on the same line and have the coordinates and , respectively. Which of the following points lies on the same line as points D and E?

Which of the following points is on the line given by the equation ?

In order to solve this, try each of the answer choices in the equation: For example, when we try (3,4), we find: This does not work. When we try all the choices, we find that only (2,4) works:

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

The equation of a line is: 2x + 9y = 71 Which of these points is on that line?

Which point lies on this line?

Test the coordinates to find the ordered pair that makes the equation of the line true:

Which of the following lines contains the point (8, 9)?

In order to find out which of these lines is correct, we simply plug in the values and into each equation and see if it balances. The only one for which this will work is

Points D and E lie on the same line and have the coordinates and , respectively. Which of the following points lies on the same line as points D and E?

Which of the following points is on the line given by the equation ?

In order to solve this, try each of the answer choices in the equation: For example, when we try (3,4), we find: This does not work. When we try all the choices, we find that only (2,4) works:

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

The equation of a line is: 2x + 9y = 71 Which of these points is on that line?

Which point lies on this line?

Test the coordinates to find the ordered pair that makes the equation of the line true:

Which of the following lines contains the point (8, 9)?

In order to find out which of these lines is correct, we simply plug in the values and into each equation and see if it balances. The only one for which this will work is

Points D and E lie on the same line and have the coordinates and , respectively. Which of the following points lies on the same line as points D and E?

Which of the following points is on the line given by the equation ?

In order to solve this, try each of the answer choices in the equation: For example, when we try (3,4), we find: This does not work. When we try all the choices, we find that only (2,4) works:

In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?

The equation of a line is: 2x + 9y = 71 Which of these points is on that line?

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

$\dpi{100} \small 5x+25y = 125$

Which point lies on this line?

In order to find out which of these lines is correct, we simply plug in the values $\dpi{100} \small x=8$ and $\dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\dpi{100} \small 3x-6=2y$

Points D and E lie on the same line and have the coordinates $\left ( 1,2\right )$ and $\left ( 5,7\right )$ , respectively. Which of the following points lies on the same line as points D and E?

Which of the following points is on the line given by the equation $y=\frac{1}{2}x+3$ ?

In order to solve this, try each of the answer choices in the equation:

$y=\frac{1}{2}x+3$

For example, when we try (3,4), we find:

$4=\frac{1}{2}(3)+3$

This does not work. When we try all the choices, we find that only (2,4) works:

$y=\frac{1}{2}x+3$

$4=\frac{1}{2}(2)+3$

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

$\dpi{100} \small 5x+25y = 125$

Which point lies on this line?

In order to find out which of these lines is correct, we simply plug in the values $\dpi{100} \small x=8$ and $\dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\dpi{100} \small 3x-6=2y$

Points D and E lie on the same line and have the coordinates $\left ( 1,2\right )$ and $\left ( 5,7\right )$ , respectively. Which of the following points lies on the same line as points D and E?

Which of the following points is on the line given by the equation $y=\frac{1}{2}x+3$ ?

In order to solve this, try each of the answer choices in the equation:

$y=\frac{1}{2}x+3$

For example, when we try (3,4), we find:

$4=\frac{1}{2}(3)+3$

This does not work. When we try all the choices, we find that only (2,4) works:

$y=\frac{1}{2}x+3$

$4=\frac{1}{2}(2)+3$

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

$\dpi{100} \small 5x+25y = 125$

Which point lies on this line?

In order to find out which of these lines is correct, we simply plug in the values $\dpi{100} \small x=8$ and $\dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\dpi{100} \small 3x-6=2y$

Points D and E lie on the same line and have the coordinates $\left ( 1,2\right )$ and $\left ( 5,7\right )$ , respectively. Which of the following points lies on the same line as points D and E?

Which of the following points is on the line given by the equation $y=\frac{1}{2}x+3$ ?

In order to solve this, try each of the answer choices in the equation:

$y=\frac{1}{2}x+3$

For example, when we try (3,4), we find:

$4=\frac{1}{2}(3)+3$

This does not work. When we try all the choices, we find that only (2,4) works:

$y=\frac{1}{2}x+3$

$4=\frac{1}{2}(2)+3$

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?