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Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #9 : How To Find Out If A Point Is On A Line With An Equation

Which point is NOT on the line y = 3x+1 ?

Possible Answers:

(-3,-8)

(-1,-4)

(-1,-2)

(1,4)

(3,10)

Correct answer:

(-1,-4)

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example, (-1,-2) is definitely on the line because when you plug it in, it creates a true equation:

y = 3x+1 plug in the and values

-2 = 3(-1)+1 multiply

-2 = -3+1

-2 = -2 this is true, so that point is on the line

The point that does not work is (-1, -4) :

-4=3(-1)+1 multiply

-4 = -3+1 subtract

$-4 \neq -2$

Since this is not true, the point is NOT on the line.

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Example Question #10 : How To Find Out If A Point Is On A Line With An Equation

The equation of a line is given below:

$y=\frac{1}{4}x + 2$

which point below can be found is NOT on the line?

Possible Answers:

(4,3)

(0,2)

(8,2)

(-8,0)

(2,2.5)

Correct answer:

(8,2)

Explanation:

To find the solution to this problem just do a quick check, pluggin in each point's x and y value into the equation. Remember coordinates are written with the x-value first, then the y-value (x,y).

If you try each point the only one that doesn't work is (8,2) !

$y=\frac{1}{4} x + 2 = \frac{1}{4}(8) +2 = \frac{8}{4} +2 = 2 + 2 = 4 \neq 2$

In other words, if the x-value is 8 the y-value should be 4!

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Example Question #81 : Coordinate Geometry

Which of the following points is on the line y=6x-5

Possible Answers:

None of these

(-4,3)

(7,2)

(-3,4)

(2,7)

Correct answer:

(2,7)

Explanation:

To ascertain if a point is on a line we must plug that coordinate pair into the equation of the line. If a true statement such as 5=5 is returned then we know that point is on our line.

y=6x-5

Choose the point you suspect is on the line.

(2,7)

7=6(2)-5

7=7

Since the equation returned a true statement the point $\mathbf{(2,7)}$ is on our line.

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Example Question #82 : Coordinate Geometry

Which of the following points is found on the line y=-2x+12 ?

Possible Answers:

(16, -20)

(-20, 10)

(18, -26)

(12, -22)

Correct answer:

(16, -20)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=16 into the given equation will give the following:

y=-2x+12

y=-2(16)+12=-32+12=-20

Thus, (16, -20) is on the line.

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Example Question #83 : Coordinate Geometry

Which of the following points is found on the line $y=\frac{1}{6}x+5$ ?

Possible Answers:

(24, 9)

(12, -3)

(60, 55)

(18, 2)

Correct answer:

(24, 9)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=24 into the given equation will give the following:

$y=\frac{1}{6}x+5$

$y=\frac{1}{6}(24)+5=4+5=9$

Thus, (24, 9) is on the line.

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Example Question #84 : Coordinate Geometry

Which of the following points is found on the line y=-10x+8 ?

Possible Answers:

(-1, 2)

(5, -58)

(20, 208)

(10, -92)

Correct answer:

(10, -92)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=10 into the given equation will give the following:

y=-10x+8

y=-10(10)+8=-100+8=-92

Thus, (10, -92) is on the line.

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Example Question #85 : Coordinate Geometry

Which of the following points is found on the line y=13x-11 ?

Possible Answers:

(13, 169)

(-10, 141)

(2, 20)

(1, 2)

Correct answer:

(1, 2)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=1 into the given equation will give the following:

y=13x-11

y=13(1)-11=13-11=2

Thus, (1, 2) is on the line.

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Example Question #86 : Coordinate Geometry

Which of the following points is found on the line $y=-\frac{3}{2}x+10$ ?

Possible Answers:

(-8, 6)

(12, 28)

(6, 19)

(-10, 25)

Correct answer:

(-10, 25)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=-10 into the given equation will give the following:

$y=-\frac{3}{2}x+10$

$y=-\frac{3}{2}(-10)+10=15+10=25$

Thus, (-10, 25) is on the line.

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Example Question #87 : Coordinate Geometry

Which of the following points is found on the line $y=\frac{1}{5}x-5$ ?

Possible Answers:

$(2, -\frac{4}{5})$

(12, 14)

(-20, -9)

$(-1, \frac{4}{5})$

Correct answer:

(-20, -9)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=-20 into the given equation will give the following:

$y=\frac{1}{5}x-5$

$y=\frac{1}{5}(-20)-5=-4-5=-9$

Thus, (-20, -9) is on the line.

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Example Question #88 : Coordinate Geometry

Which of the following points is found on the line 3x+4y=5 ?

Possible Answers:

$(12, -\frac{31}{4})$

$(0, -\frac{3}{4})$

$(2, -\frac{1}{2})$

(-1, 12)

Correct answer:

$(12, -\frac{31}{4})$

Explanation:

Start by rewriting the equation into slope-intercept form.

3x+4y=5

4y=-3x+5

$y=-\frac{3}{4}x+\frac{5}{4}$

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=12 into the given equation will give the following:

$y=-\frac{3}{4}x+\frac{5}{4}$

$y=-\frac{3}{4}(12)+\frac{5}{4}=-9+\frac{5}{4}=-\frac{31}{4}$

Thus, $(12, -\frac{31}{4})$ is on the line.

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Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #9 : How To Find Out If A Point Is On A Line With An Equation

Example Question #10 : How To Find Out If A Point Is On A Line With An Equation

Example Question #81 : Coordinate Geometry

Example Question #82 : Coordinate Geometry

Example Question #83 : Coordinate Geometry

Example Question #84 : Coordinate Geometry

Example Question #85 : Coordinate Geometry

Example Question #86 : Coordinate Geometry

Example Question #87 : Coordinate Geometry

Example Question #88 : Coordinate Geometry

All Intermediate Geometry Resources

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