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GED Math : Algebra

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Example Questions

Example Question #33 : Slope Intercept Form

Find the slope of the line perpendicular to the line: $y = \frac{3}{4}x + 10$

Possible Answers:

$-\frac{3}{4}$

$\frac{1}{4}$

$-\frac{4}{3}$

$\frac{3}{4}$

$\frac{3}{4}y$

Correct answer:

$-\frac{4}{3}$

Explanation:

Remember that the slopes of perpendicular lines are each other's negative reciprocal.

To find the negative reciprocal of a number, we put it into fraction form, invert the numerator and the denominator, and negate the result.

For example: $\frac{x}{y}$

$\frac{y}{x}$ (invert the numerator and denominator)

$-\frac{y}{x}$ (negate the result)

In our example, the slope of our equation is $\frac{3}{4}$

$\frac{4}{3}$ (invert the numerator and denominator)

$-\frac{4}{3}$ (negate the result)

Therefore, the slope of a line perpendicular to the line $y = \frac{3}{4}x + 10$ is ${\color{DarkGreen} -}\frac{{\color{DarkGreen} }{\color{DarkGreen} 4}}{{\color{DarkGreen} 3}}$

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Example Question #34 : Slope Intercept Form

Which line is parallel to the line $y = \frac{3}{7}x + 19$ ?

Possible Answers:

$y = -\frac{3}{7}x + 19$

$y = \frac{4}{7}x + 31$

$y = \frac{7}{3}x + 19$

$y = -\frac{7}{3}x + 19$

$y = \frac{3}{7}x + 31$

Correct answer:

$y = \frac{3}{7}x + 31$

Explanation:

Parallel lines have identical slopes. The y-intercept, in this case, is irrelevant.

The line which has the same slope as $y = \frac{3}{7}x + 19$ is:

$y = \frac{3}{7}x + 31$

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Example Question #35 : Slope Intercept Form

Given two points of a line (0,3),(6,15) with the y-intercept , write the equation of the line in slope-intercept form.

Possible Answers:

y = 2x + 3

y = 2

y = 2x - 3

y = -2x + 3

y = 6x + 15

Correct answer:

y = 2x + 3

Explanation:

In our equation y = mx + b , we need to find the slope, , and the y-intercept, .

To find the slope of a line given two points, $(x_{1},x_{2}),(y_{1},x_{1})$ , we have our slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, given (0,3),(6,15) , we can find the slope by substituting those values into our slope formula:

$m = \frac{15-3}{6-0}$ $=\frac{12}{6}=2$

Our y-intercept was given as , so, b = 3

We have our and our , so the answer is y = 2x + 3

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Example Question #36 : Slope Intercept Form

Put the following equation, which is in slope-intercept form, into standard form:

y = -11x + 16

Possible Answers:

$x = -\frac{y}{11}+\frac{16}{11}$

y - 16 = -11x

y + 11x - 16 = 0

y = -16x + 11

11x + y = 16

Correct answer:

11x + y = 16

Explanation:

A linear equation in standard form is represented by: Ax + By = C

In our equation, y = -11x + 16 , we can arrange these values to get it into its standard form:

$y {\color{Blue} +11x} = -11x {\color{Blue} +11x} + 16$ (add 11x to both sides)

y + 11x = 16

Or, 11x + y = 16 , which is in the form Ax + By = C

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Example Question #37 : Slope Intercept Form

In the equation 6y = 6x - 24 , find the slope and y-intercept.

Possible Answers:

m = 6x

b = -24

m= 6

b = -24

m=1

b = -4

m = x

b = -4

m = x

b = -24

Correct answer:

m=1

b = -4

Explanation:

First, get the equation into slope-intercept form y = mx +b

$1) \frac{6}{{\color{Red} 6}}y = \frac{6}{{\color{Red} 6}}x -\frac{24}{6}$ (divide both sides by 6)

2) y = x - 4

We can clearly see the y-intercept as b = 4

For the slope, notice that there is an invisible coefficient of in front of the . That is our slope. m = 1

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Example Question #38 : Slope Intercept Form

Arrange this linear equation so it is in slope-intercept form:

-5x - 4y + 3 = 3x

Possible Answers:

-8x - 4y + 3 = 0

-4y + 3 = 8x

$x =- \frac{1}{2} + \frac{3}{8}$

-8x -4y = 3

$y = -2x + \frac34{}{}$

Correct answer:

$y = -2x + \frac34{}{}$

Explanation:

The slope-intercept form of a line is represented as:

y = mx + b

To rearrange -5x - 4y + 3 = 3x into y = mx + b form, we must get by itself.

1) $-5x {\color{Blue} +} {\color{Blue} 5x} - 4y +3 {\color{Blue} -3} = 3x {\color{Blue} +5x -3}$ (add to and subtract from both sides)

2) -4y = 8x - 3

3) $\frac{-4}{{\color{Red} -4}}y = \frac{8}{{\color{Red} -4}}x + \frac{3}{{\color{Red} -4}}$ (divide both sides by )

4) $y = -2x + \frac{3}{4}$

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Example Question #39 : Slope Intercept Form

Rearrange the following equation, which is in its standard form, into slope-intercept form: $\frac{3}{5}x + \frac{1}{30}y = \frac{1}{6}$

Possible Answers:

y = -18x + 5

$\frac{1}{30}y = -\frac{3}{5}x + \frac{1}{6}$

$30y = -\frac{5}{3}x + 6$

$\frac{3}{5}x = \frac{1}{6} - \frac{1}{30}y$

$y = -\frac{3}{5}x + \frac{1}{6}$

Correct answer:

y = -18x + 5

Explanation:

Recall that our slope-intercept form is y = mx + b

First, we get the term by itself:

$\frac{3}{5}x {\color{Blue} -\frac{3}{5}x} + \frac{1}{30}y = \frac{1}{6} {\color{Blue} -\frac{3}{5}x}$ (subtract $\frac{3}{5}x$ from both sides)

$2) \frac{1}{30}y = -\frac{3}{5}x + \frac{1}{6}$

Then:

$3) {\color{Red} 30} \cdot\frac{1}{30}y = {\color{Red} 30}\cdot-\frac{3}{5}x + {\color{Red} 30}\cdot\frac{1}{6}$ (multiply both sides by the reciprocal of the coefficient)

4) y = -18x + 5

Our answer is ${\color{DarkGreen} y = -18x + 5}$

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Example Question #40 : Slope Intercept Form

Which line is parallel to 5x + y = 7 ?

Possible Answers:

y = 7

$y = -\frac{1}{5}x + 7$

y = -5x + 1

y = 5x + 1

$y = \frac{1}{5}x + 7$

Correct answer:

y = -5x + 1

Explanation:

You may know that parallel lines have the same slope. With that in mind, it may be tempting to see that there and find an equation with and a different y-intercept.

Be careful of that trap! Notice that equation is written in STANDARD form, and to find the slope of a line we must get it into slope-intercept form, y = mx + b

Arranging the equation 5x + y = 7 into slope-intercept form, we see that we get y = -5x + 7

Our slope is -5x , so a line parallel could be y = -5x + 1 , one of our choices.

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Example Question #41 : Slope Intercept Form

What identification mistake(s), if any, did this student make?

3y = 4x + 21

m = 4

b = 7

Possible Answers:

The slope, , is and the y-intercept, , is

The slope, , is correct..

The y-intercept, , is correct.

After dividing both sides by , the student neglected to divide the -value by , as well. So the slope was incorrect. It should be $m = \frac{4}{3}$

The y-intercept, b=7 , is correct.

The slope, , is correct.

After dividing both sides by , the student should not have divided the y-intercept, b = 21 , by . The y-intercept is incorrect.

The student should have put it in standard form to find the slope and y-intercept.

Correct answer:

After dividing both sides by , the student neglected to divide the -value by , as well. So the slope was incorrect. It should be $m = \frac{4}{3}$

The y-intercept, b=7 , is correct.

Explanation:

The student was correct in the attempt to get the equation into slope-intercept form, y = mx + b by dividing by on both sides.

The slope should have been: $m = \frac{4}{3}$

The y-intercept was correct in being: b = 7

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Example Question #41 : Linear Algebra

What is the equation of the line that goes through the points (-1, 6) and (2, -6) ?

Possible Answers:

y=-4x+2

y=4x-2

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

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

Correct answer:

y=-4x+2

Explanation:

Start by finding the slope of the line.

Recall how to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Using the given points,

$\text{Slope}=\frac{-6-6}{2-(-1)}=\frac{-12}{3}=-4$

Now, we can write the equation for the line as the following:

y=-4x+b , where is the y-intercept that we still need to find.

Take one of the points and plug it into the equation for and , then solve for .

Using the point (-1, 6) ,

6=-4(-1)+b

6=4+b

b=2

Thus, the equation of the line must be y=-4x+2

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GED Math : Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #33 : Slope Intercept Form

Example Question #34 : Slope Intercept Form

Example Question #35 : Slope Intercept Form

Example Question #36 : Slope Intercept Form

Example Question #37 : Slope Intercept Form

Example Question #38 : Slope Intercept Form

Example Question #39 : Slope Intercept Form

Example Question #40 : Slope Intercept Form

Example Question #41 : Slope Intercept Form

Example Question #41 : Linear Algebra

All GED Math Resources

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