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GED Math : Algebra

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Example Questions

Example Question #3 : Points And Lines

4x - 3y = 17

2x+y = 13

What is the -coordinate of the point at which the lines of these two equations intersect?

Possible Answers:

$y = 1 \frac{4}{5}$

The lines of the equations do not intersect.

$y = 7 \frac{1}{2}$

y = -6

y = 33

Correct answer:

$y = 1 \frac{4}{5}$

Explanation:

The elimination method will work here. Multiply the second equation by on both sides, then add to the first:

2x+y = 13

$-2 \left (2x+y \right )= -2 \left ( 13 \right )$

-4x-2y = -26

$\underline{4x - 3y = 17}$

-5y = -9

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

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Example Question #4 : Points And Lines

4x + 3y = 17

2x+y = 13

What is the -coordinate of the point at which the lines of these two equations intersect?

Possible Answers:

The lines do not intersect at any point.

y = 2

$y = -1\frac{4}{5}$

y = -43

y = -9

Correct answer:

y = -9

Explanation:

The elimination method will work here. Multiply the second equation by on both sides, then add to the first:

2x+y = 13

$-2 \left (2x+y \right )= -2 \left ( 13 \right )$

-4x-2y = -26

$\underline{4x + 3y = 17}$

y = -9

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Example Question #5 : Points And Lines

4x - 3y = 17

2x+y = 13

What is the -coordinate of the point at which the lines of these two equations intersect?

Possible Answers:

$x=11\frac{1}{5}$

x=5

x = 10

$x = 5\frac{3}{5}$

Correct answer:

$x = 5\frac{3}{5}$

Explanation:

The elimination method will work here. Multiply the second equation by 3 on both sides, then add to the first:

2x+y = 13

$3 \left (2x+y \right )= 3 \left ( 13 \right )$

6x+ 3y = 39

$\underline{4x - 3y = 17}$

$10x \; \; \; \; \; = 56$

$x =56 \div 10$

$x = 5\frac{3}{5}$

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Example Question #5 : Points And Lines

Which of the following is an equation for the line between the points (5,1) and (8,10) ?

Possible Answers:

y=5x+10

y=3x-10

y=3x-14

y=4x+15

y=3x+9

Correct answer:

y=3x-14

Explanation:

Probably the easiest way to solve this question is to use the point-slope form of an equation. Remember that for that format, you need a point and the slope of the line. (Pretty obvious, given the name!) For a point (x_1,y_1) , the point-slope form is:

y-y_1=m(x-x_1) , where is the slope

Now, recall that the slope is calculated from two points using the formula:

$\frac{rise}{run} = \frac{y_2-y_1}{x_2-x1}$

For our data, this is:

$\frac{10-1}{8-5}=\frac{9}{3}=3$

Thus, for your point-slope form of the line, you get the equation:

y-10=3(x-8)

Just simplify things now...

y-10=3x-24

y=3x-14

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Example Question #6 : Points And Lines

Which of the following is an equation for the line between the points (3,7) and (10,19) ?

Possible Answers:

26y=13x+734

$y=\frac{12}{7}x + \frac{62}{7}$

$y=\frac{12}{7}x + \frac{13}{7}$

12y=5x+3

y=13x+26

Correct answer:

$y=\frac{12}{7}x + \frac{13}{7}$

Explanation:

y-y_1=m(x-x_1) , where is the slope

Now, recall that the slope is calculated from two points using the formula:

$\frac{rise}{run} = \frac{y_2-y_1}{x_2-x1}$

For our data, this is:

$\frac{19-7}{10-3}=\frac{12}{7}$

Now, that is an awkward slope, but just be careful with the simplification. For the point-slope form of the line, you get the equation:

$y-7=\frac{12}{7}(x-3)$

Just simplify things now...

$y-7=\frac{12}{7}x - 3 * \frac{12}{7}$

$y-7=\frac{12}{7}x - \frac{36}{7}$

$y=\frac{12}{7}x - \frac{36}{7} + 7$

Now, find a common denominator for the fractions. (It is .)

$y=\frac{12}{7}x - \frac{36}{7} + \frac{49}{7}$

$y=\frac{12}{7}x + \frac{13}{7}$

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Example Question #5 : Points And Lines

Which of the following lines contains the point (1,9) ?

Possible Answers:

x-9y=77

17x-3y=3

y=x+9

3y - 15 =12x

4x+12y=-53

Correct answer:

3y - 15 =12x

Explanation:

To solve for a question like this, the easiest thing to do is to plug in your and values to see what happens. If you get two numbers equal to each other when they are, in fact, unequal, you do not have a working case.

For example, consider the wrong option, y=x+9

Substitute in your values, and you get:

9=1+9 or 9=10

Now, for your correct option, you get:

3y - 15 =12x

3 * 9 - 15 =12*1

27-15=12

12=12

This certainly makes sense! It also means that the point is on the line in question!

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Example Question #5 : Points And Lines

Which of the following points is on the line y=-x+7 ?

Possible Answers:

(5,-2)

(8,1)

(-7,0)

(4,3)

(3,10)

Correct answer:

(4,3)

Explanation:

Upon substitution of the answer choices, we will need to satisfy the equation, by plugging in the x and y-values of the points given.

$(8,1): 1\neq-8+7$

$(5,-2): -2\neq -5+7$

$(3,10): 10 \neq -3+7$

$(-7,0): 0\neq -(-7)+7$

The answer is: (4,3)

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Example Question #9 : Points And Lines

Find the equation of the line given the two points (0,2) and (-2,3) .

Possible Answers:

$y=-\frac{5}{2}x+2$

$y=\frac{5}{2}x+2$

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

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

$y=-\frac{5}{2}x-2$

Correct answer:

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

Explanation:

The equation of a line in slope-intercept form is y=mx+b .

Write the formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

Substitute the points.

$\frac{3-2}{-2-0} = -\frac{1}{2}$

The y-intercept from the point (0,2) means that b=2 .

The equation of the line is: $y=-\frac{1}{2}x+2$

The answer is: $y=-\frac{1}{2}x+2$

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Example Question #11 : Points And Lines

Given the points (9,-1) and (3,9) , what is the equation of the line?

Possible Answers:

$y= \frac{3}{2}x+14$

$y+1 = -\frac{5}{3}(x-9)$

3x-2y =-14

$y+1 = -\frac{10}{3}(x-9)$

3x-2y =14

Correct answer:

$y+1 = -\frac{5}{3}(x-9)$

Explanation:

The equation of the line is defined in the following forms:

Point-slope form: y-y_1 = m(x-x_1)

Standard form: Ax+By=C

Slope intercept form: y=mx+b

Find the slope of the two points using the slope formula.

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{9-(-1)}{3-9} = \frac{10}{-6} = -\frac{5}{3}$

Using the slope and any point (9,-1) or (3,9) , we can substitute either into the point-slope form.

$y-(-1) = -\frac{5}{3}(x-9)$

The answer is: $y+1 = -\frac{5}{3}(x-9)$

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Example Question #11 : Points And Lines

Find the slope given the two points: (2,-3) and (6,-9)

Possible Answers:

$-\frac{3}{2}$

$-\frac{1}{5}$

$-\frac{2}{5}$

Correct answer:

$-\frac{3}{2}$

Explanation:

Write the slope formula.

$m = \frac{y_2-y_1}{x_2-x_1}$

Substitute the points.

$m = \frac{-9-(-3)}{6-2} = \frac{-6}{4} = -\frac{3}{2}$

The answer is: $-\frac{3}{2}$

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All GED Math Resources

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GED Math : Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #3 : Points And Lines

Example Question #4 : Points And Lines

Example Question #5 : Points And Lines

Example Question #5 : Points And Lines

Example Question #6 : Points And Lines

Example Question #5 : Points And Lines

Example Question #5 : Points And Lines

Example Question #9 : Points And Lines

Example Question #11 : Points And Lines

Example Question #11 : Points And Lines

All GED Math Resources

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