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GED Math : Linear Algebra

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Example Questions

Example Question #21 : Linear Algebra

Write the equation in slope intercept form:

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

Possible Answers:

$y=-\frac{3}{2}x-12$

$y=\frac{3}{2}x+12$

2x+3y = 24

$y=-\frac{3}{2}x+12$

3x+2y =12

Correct answer:

$y=-\frac{3}{2}x+12$

Explanation:

To write the equation in slope intercept form, first recall the general form for slope intercept.

y=mx+b

where represents the slope and represents the y-intercept.

Given the equation in this question,

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

first subtract the $\frac{x}{2}$ .

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

Now to isolate multiply both sides by three.

$3\cdot \frac{y}{3} =3\left( -\frac{x}{2}+4\right)$

Distribute the three to all parts within the parentheses.

$y=-\frac{3}{2}x+12$

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Example Question #21 : Slope Intercept Form

Rewrite the equation in slope-intercept form: 2x+5y=3

Possible Answers:

$y=-\frac{2}{5}x +\frac{3}{5}$

$y=-\frac{5}{2}x +\frac{5}{3}$

$y=\frac{2}{5}x -\frac{3}{5}$

$y=\frac{5}{2}x -\frac{5}{3}$

$y=\frac{2}{5}x +\frac{3}{5}$

Correct answer:

$y=-\frac{2}{5}x +\frac{3}{5}$

Explanation:

The slope-intercept form is y=mx+b .

Subtract from both sides.

2x+5y-2x=3-2x

5y = -2x+3

Divide by five on both sides.

$\frac{5y}{5} = \frac{-2x+3}{5}$

Simplify both sides.

The answer is: $y=-\frac{2}{5}x +\frac{3}{5}$

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Example Question #21 : Linear Algebra

Suppose the slope of a line is 5, and the x-intercept is 2. What must be the equation of the line in slope-intercept form?

Possible Answers:

y=5x+2

y=5x-7

y=5x-2

y=5x-10

y=5x+10

Correct answer:

y=5x-10

Explanation:

The slope intercept form is: y=mx+b

The x-intercept of 2 means the point given is: (2,0)

Substitute this point and the slope to determine the value of , or the y-intercept.

0=5(2)+b

0=10+b

b=-10

Substitute this value and the slope back into y=mx+b .

The answer is: y=5x-10

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Example Question #23 : Slope Intercept Form

Rewrite the following equation to slope-intercept format: 2x+9y = 31

Possible Answers:

$y= -\frac{2}{9}x+\frac{31}{2}$

$y= \frac{9}{2}x+31$

$y= -\frac{9}{2}x+31$

$y= -\frac{2}{9}x+\frac{31}{9}$

$y= -\frac{2}{9}x+31$

Correct answer:

$y= -\frac{2}{9}x+\frac{31}{9}$

Explanation:

The slope intercept form of a line is: y=mx+b

Subtract from both sides.

2x+9y -2x= 31-2x

9y = -2x+31

Divide by 9 on both sides.

$\frac{9y }{9}= \frac{-2x+31}{9}$

The answer is: $y= -\frac{2}{9}x+\frac{31}{9}$

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Example Question #21 : Linear Algebra

Rewrite the following equation in slope-intercept form: 2x-9y = -1

Possible Answers:

$y=\frac{1}{9}x +\frac{2}{9}$

$y=-\frac{1}{9}x +\frac{2}{9}$

$y=\frac{2}{9}x +\frac{1}{9}$

$y=\frac{2}{9}x -\frac{1}{9}$

$y=-\frac{2}{9}x +\frac{1}{9}$

Correct answer:

$y=\frac{2}{9}x +\frac{1}{9}$

Explanation:

The slope-intercept form of a line is: y=mx+b

Subtract from both sides.

2x-9y -(2x)= -1-(2x)

Simplify both sides.

-9y= -2x-1

Divide by negative nine on both sides.

$\frac{-9y}{-9}= \frac{-2x-1}{-9}$

The equation is: $y=\frac{2}{9}x +\frac{1}{9}$

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Example Question #21 : Slope Intercept Form

Rewrite the equation in slope-intercept form. 4x-2y =7

Possible Answers:

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

$y= 2x-\frac{7}{4}$

$y= 4x-\frac{7}{2}$

$y= 2x-\frac{7}{2}$

$y= 2x+\frac{7}{2}$

Correct answer:

$y= 2x-\frac{7}{2}$

Explanation:

The slope-intercept form is: y=mx+b

Rearrange this equation. Subtract from both sides.

4x-2y -4x=7-4x

-2y = -4x+7

Divide by negative two on both sides.

$\frac{-2y }{-2}=\frac{ -4x+7}{-2}$

The answer is: $y= 2x-\frac{7}{2}$

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Example Question #22 : Linear Algebra

Write the equation in slope-intercept form: 2x-9y =3y

Possible Answers:

$y=- \frac{1}{6}x$

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

$\textup{The answer is not given.}$

$y= -\frac{1}{3}x$

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

Correct answer:

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

Explanation:

The slope intercept form is: y=mx+b

Add on both sides.

2x-9y+9y =3y+9y

2x = 12y

Divide by 12 on both sides.

$\frac{2x }{12}= \frac{12y}{12}$

Reduce the fractions.

The answer is: $y= \frac{1}{6}x$

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Example Question #23 : Linear Algebra

Which of the following represents a linear equation in slope-intercept form?

Possible Answers:

y=-15x-125

y=-3x^2-12x+4

y-6=3(x+4)

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

Correct answer:

y=-15x-125

Explanation:

Which of the following represents a linear equation in slope-intercept form?

Slope intercept form is commonly written as:

y=mx+b

Where m is our slope and b is our intercept. Note that m and b can be negative.

Now, we are asked to find the equation which is in slope intercept form. This means, we want an option which looks like the above form.

First, rule out anything that isn't linear. Linear equation describe a straight line, whereas other equations may be curved.

y=-3x^2-12x+4

Is a quadratic equation, so it is not our answer

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

Is not linear either, it is a reciprocal function.

Thus, we are left with:

y-6=3(x+4)

y=-15x-125

Of these, only the second is in the correct form. The first could be rearranged to be in slope-intercept form, but it is not currently.

So, our answer is:

y=-15x-125

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Example Question #24 : Linear Algebra

What is the slope of the line 3x-8y=24 ?

Possible Answers:

$\frac{3}{8}$

$\frac{8}{3}$

Correct answer:

$\frac{3}{8}$

Explanation:

Start by rewriting the equation in slope-intercept form.

3x-8y=24

-8y=-3x+24

$y=\frac{3}{8}x+3$

Recall that in the slope intercept form, y=mx+b , is the slope. For the given equation, $m=\frac{3}{8}$ . The slope must be $\frac{3}{8}$ .

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Example Question #22 : Linear Algebra

What is the y-intercept in the following linear equation?

y = 4x - 16

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept, we must have our linear equation in slope-intercept form:

y = mx + b , where represents the y-intercept

Our equation is already in this form:

y = 4x - 16

Therefore, our y-intercept is

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GED Math : Linear Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Linear Algebra

Example Question #21 : Slope Intercept Form

Example Question #21 : Linear Algebra

Example Question #23 : Slope Intercept Form

Example Question #21 : Linear Algebra

Example Question #21 : Slope Intercept Form

Example Question #22 : Linear Algebra

Example Question #23 : Linear Algebra

Example Question #24 : Linear Algebra

Example Question #22 : Linear Algebra

All GED Math Resources

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