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GED Math : Linear Algebra

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Example Questions

Example Question #6 : Finding Slope And Intercepts

What is the x-intercept of 2y+3x=159 ?

Possible Answers:

$\frac{159}{2}$

$\frac{159}{5}$

No x-intercept

Correct answer:

Explanation:

Remember, to find the x-intercept, you need to set equal to zero. Therefore, you get:

3x=159

Simply solving, this is x=53

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Example Question #6 : Finding Slope And Intercepts

Find the slope of the line that has the equation: 2x-3y=4

Possible Answers:

$\frac {4}{3}$

$-\frac {2}{3}$

$\frac {2}{3}$

Correct answer:

$\frac {2}{3}$

Explanation:

Step 1: Move x and y to opposite sides...

We will subtract 2x from both sides...

Result, -3y=-2x+4

Step 2: Recall the basic equation of a line...

y=mx+b , where the coefficient of y is .

Step 3: Divide every term by to change the coefficient of y to :

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

Step 4: Reduce...

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

Step 5: The slope of a line is the coefficient in front of the x term...

So, the slope is $\frac {2}{3}$

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Example Question #1 : Finding Slope And Intercepts

Find the slope of the following equation: y=-9(-x+6)

Possible Answers:

$\frac{1}{9}$

$\textup{The slope cannot be determined.}$

Correct answer:

Explanation:

In order to find the slope, we will need the equation in slope-intercept form.

y=mx+b

Distribute the negative nine through the binomial.

y=(-9)(-x)+(-9)(6) = 9x-54

The slope is:

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Example Question #11 : Finding Slope And Intercepts

What is the y-intercept of the following equation? -3x= y+7

Possible Answers:

$\frac{7}{3}$

$-\frac{3}{7}$

$-\frac{7}{3}$

Correct answer:

Explanation:

The y-intercept is the value of when x=0 .

Substitute the value of zero into , and solve for .

-3(0)= y+7

0 = y+7

Subtract 7 from both sides.

0 -7= y+7-7

y=-7

The answer is:

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Example Question #11 : Finding Slope And Intercepts

Find the slope and y-intercept, respectively, given the following equation:

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

Possible Answers:

$-\frac{2}{3}, \frac{1}{2}$

$\frac{1}{2}, \frac{1}{3}$

$\frac{1}{2}, -\frac{1}{3}$

$-\frac{1}{2}, -\frac{1}{3}$

$\frac{2}{3}, \frac{1}{2}$

Correct answer:

$\frac{1}{2}, \frac{1}{3}$

Explanation:

Rewrite the equation in slope-intercept format: y=mx+b

Divide by negative two on both sides. This is also the same as multiplying both sides by negative half.

$(-2y) (-\frac{1}{2})= (-\frac{1}{2})(-\frac{2}{3}-x)$

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

Rearrange the terms.

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

The slope is: $\frac{1}{2}$

The y-intercept is: $\frac{1}{3}$

The answer is: $\frac{1}{2}, \frac{1}{3}$

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Example Question #12 : Finding Slope And Intercepts

Find the slope of the following function: y=-5(-5x+2x)

Possible Answers:

Correct answer:

Explanation:

Simplify the terms of the equation by distribution.

y=-5(-5x+2x) = 25x-10x

y= 25x-10x

Subtract the terms.

y=15x

The equation is now in slope-intercept form, where b=0 .

The slope is .

The answer is .

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Example Question #14 : Finding Slope And Intercepts

What is the slope of the following equation? x+9y = -7

Possible Answers:

$-\frac{9}{7}$

$-\frac{7}{9}$

$-\frac{1}{9}$

Correct answer:

$-\frac{1}{9}$

Explanation:

To determine the slope, we will need the equation in slope-intercept form.

y=mx+b

Subtract on both sides.

x+9y -x= -7-x

9y = -x-7

Divide by 9 on both sides.

$\frac{9y }{9}= \frac{-x-7}{9}$

Split both terms on the right side.

$y= -\frac{1}{9}x-\frac{7}{9}$

The slope is: $-\frac{1}{9}$

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Example Question #13 : Finding Slope And Intercepts

Identify the y-intercept: -2x+2y = 3y

Possible Answers:

$\frac{2}{3}$

$\textup{No solution.}$

$\frac{3}{2}$

Correct answer:

Explanation:

In order to find the y-intercept, we will need to let x=0 and solve for .

-2(0)+2y = 3y

2y=3y

Subtract from both sides. Do NOT divide by on both sides.

2y-2y=3y-2y

y=0

The answer is:

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Example Question #13 : Finding Slope And Intercepts

What is the x-intercept of the following equation? y=-5x+3

Possible Answers:

$\frac{3}{5}$

$-\frac{3}{5}$

$-\frac{5}{3}$

$\frac{5}{3}$

Correct answer:

$\frac{3}{5}$

Explanation:

In order to find the x-intercept, we will need to let y=0 , and solve for .

0=-5x+3

Add on both sides.

0+5x=-5x+3+5x

5x=3

Divide by five on both sides.

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

The answer is: $\frac{3}{5}$

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Example Question #14 : Finding Slope And Intercepts

A line on the coordinate plane has as its equation 3x+ 8y = 28 .

Which of the following is its slope?

Possible Answers:

$\frac{8}{3}$

$-\frac{8}{3}$

$-\frac{3}{8}$

$\frac{3}{8}$

Correct answer:

$-\frac{3}{8}$

Explanation:

Rewrite the equation in the slope-intercept form y = mx+b , with the slope, as follows:

Subtract from both sides:

3x+ 8y = 28

3x+ 8y - 3x = 28 - 3x

8y = -3x + 28

Multiply both sides by $\frac{1}{8}$ , distributing on the right:

$\frac{1}{8} \cdot 8y =\frac{1}{8} \cdot \left ( -3x + 28 \right )$

$y =\frac{1}{8} \cdot ( -3x) +\frac{1}{8} \cdot 28$

$y =\frac{1}{8} \cdot \frac{ -3}{1}\cdot x +\frac{1}{8} \cdot \frac{28}{1}$

$y =- \frac{3}{8} x +\frac{28}{8}$

$y =- \frac{3}{8} x +\frac{7}{2}$

In the slope-intercept form, the coefficient of is the slope . This is $- \frac{3}{8}$ .

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GED Math : Linear Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #6 : Finding Slope And Intercepts

Example Question #6 : Finding Slope And Intercepts

Example Question #1 : Finding Slope And Intercepts

Example Question #11 : Finding Slope And Intercepts

Example Question #11 : Finding Slope And Intercepts

Example Question #12 : Finding Slope And Intercepts

Example Question #14 : Finding Slope And Intercepts

Example Question #13 : Finding Slope And Intercepts

Example Question #13 : Finding Slope And Intercepts

Example Question #14 : Finding Slope And Intercepts

All GED Math Resources

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