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Algebra 1 : Slope and Line Equations

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Example Questions

Example Question #171 : Equations Of Lines

What is the slope of the line depicted by the equation?

6x+3y=15

Possible Answers:

$m=\frac{2}{5}$

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

m=-2

$m=\frac{5}{2}$

Correct answer:

m=-2

Explanation:

The equation is written in standard from: $\small Ax+By=C$ . In this format, the slope is $\small -\frac{A}{B}$ .

6x+3y=15

In our equation, $\small A=6$ and $\small B=3$ .

$\small m=-\frac{A}{B}=-\frac{6}{3}$

$\small -\frac{6}{3}=-2$

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Example Question #13 : How To Find Slope Of A Line

Find the slope of the line defined by the equation 4x - 6y = 15 .

Possible Answers:

$-\frac{3}{2}$

$\frac{2}{3}$

$\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

4x - 6y = 15

-4x + 4x - 6y = -4x + 15

- 6y = -4x + 15

$- 6y \div (-6)=\left ( -4x + 15 \right )\div (-6)$

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

The slope is the coefficient of : $m = \frac{2}{3}$

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Example Question #11 : How To Find Slope Of A Line

Find the slope of the line that includes points (5,-4) and (8,-2) .

Possible Answers:

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{6}{13}$

$\frac{3}{2}$

Correct answer:

$\frac{2}{3}$

Explanation:

Use the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-2-(-4)}{8-5} = \frac{2}{3}$

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Example Question #12 : How To Find Slope Of A Line

Find the slope of the line that includes points (5,4) and (8,-2) .

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{10}$

$\frac{6}{13}$

$\frac{13}{6}$

Correct answer:

Explanation:

Use the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-2-4}{8-5} = \frac{-6}{3} = -2$

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Example Question #16 : How To Find Slope Of A Line

Line is a straight line that passes through these points on a graph:(-4,0) (0,3) and (4,6). What is the slope of line ?

Possible Answers:

There is no straight line that passes through these three points.

$-\frac{4}{3}$

$\frac{3}{4}$

$-\frac{3}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{3}{4}$

Explanation:

To calculate the slope of a line, we pick two points, and calculate the change in divided by the change in . To calculate the change in value, we use subtraction. So,

slope = $\frac{\text{Change in Y}}{\text{Change in X}} = \frac{y_2-y_1}{x_2-x_1}$

So we can pick any two points and plug them into this formula. Let's choose (0,3) and (4,6). We get

$\frac{6-3}{4-0}= \frac{3}{4}$

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Example Question #17 : How To Find Slope Of A Line

The following equation describes a straight line.

y=-2x-3

Identify the slope and y-intercept of the line.

Possible Answers:

Slope: $\small -3$

Y-intercept: $\small (0,-2)$

Slope: $\small -2$

Y-intercept: $\small (0,-3)$

Slope: $\small -2$

Y-intercept: $\small (-3,0)$

None of these

Slope: $\small -3$

Y-intercept: $\small (-2,0)$

Correct answer:

Slope: $\small -2$

Y-intercept: $\small (0,-3)$

Explanation:

The general formula of a straight line is y=mx+b , where $\small m$ is the slope and $\small b$ is the y-intercept.

To evaluate our original equation, we can compare it to this formula.

y=mx+b

y=-2x-3

The slope is $\small -2$ and the y-intercept is at $\small -3$ . Since the y-intercept is a point on the line, it is written as $\small (0,-3)$ .

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Example Question #18 : How To Find Slope Of A Line

Find the slope of the line defined by the equation 2x + 6y = 15 .

Possible Answers:

$\frac{1}{3}$

$- \frac{1}{3}$

Correct answer:

$- \frac{1}{3}$

Explanation:

Rewrite in slope-intercept form:

2x + 6y = 15

-2x + 2x + 6y = -2x +15

6y = -2x +15

$6y \div 6= \left (-2x +15 \right )\div 6$

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

The slope is the coefficient of :

$m = - \frac{1}{3}$

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Example Question #11 : How To Find Slope Of A Line

Identify the slope and y-intercept of the following function.

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

Possible Answers:

Slope: $\frac{1}{3}$

Y-intercept: (0,-2)

Slope:

Y-intercept: (0,3)

Slope: $-\frac{1}{3}$

Y-intercept: (0,-2)

Slope:

Y-intercept: $(0,-\frac{1}{2})$

Slope:

Y-intercept: $(0,\frac{1}{2})$

Correct answer:

Slope: $-\frac{1}{3}$

Y-intercept: (0,-2)

Explanation:

This function describes a straight line. We can compare the given equation with the formula for a straight line in slope-intercept form.

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

y=mx+b

In the formula, is the slope and is the y-intercept. Looking at our given equation, we can see that $m=-\frac{1}{3}$ and b=-2 .

Since the y-intercept is a point, we want to write it in point notation: (0,-2)

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Example Question #20 : How To Find Slope Of A Line

Determine the slope and y-intercept of the following equation.

1-10x+5y=2

Possible Answers:

None of these

Slope:

Y-intercept: $(0,\frac{1}{5})$

Slope: $\frac{1}{2}$

Y-intercept: (0,-3)

Slope:

Y-intercept: $(0,\frac{1}{9})$

Slope:

Y-intercept: $(0,\frac{1}{2})$

Correct answer:

Slope:

Y-intercept: $(0,\frac{1}{5})$

Explanation:

1-10x+5y=2

You see that this equation is not written explicitly in terms of . Before we can determine the slope and y-intercept, we need to write the equation explicitly in terms of by solving for .

First, add 10x to both sides.

1-10x+10x+5y=10x+2

1+5y=10x+2

Then subtract to both sides.

1-1+5y=10x+2-1

5y=10x+1

Finally, divide by .

$\frac{5y}{5}=\frac{10x+1}{5}$

$y=2x+\frac{1}{5}$

Now that the equation is explicitly in terms of , we can compare it to the general formula of a straight line in slope-intercept form.

y=mx+b

In this equation, is equal to the slope and is equal to the y-intercept. Comparing our given equation to the formula, we can see that m=2 and $b=\frac{1}{5}$ .

Since the y-intercept is a point, we will want to write it in point notation: $(0,\frac{1}{5})$ .

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Example Question #21 : How To Find Slope Of A Line

There are two points: (-2,4) and (3,-1) .

If these points are connected by a straight line, what is the slope of this straight line?

Possible Answers:

Correct answer:

Explanation:

To determine the slope, we use the following formula.

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

In the formula, the two points making up that slope are (x_1,y_1) and (x_2,y_2) . In our case, our two points are (-2,4) and (3,-1) . Using these values in the formula allows us to solve for the slope.

$m=\frac{-1-4}{3-(-2)}=\frac{-5}{5}=-1$

The slope is .

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Algebra 1 : Slope and Line Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #171 : Equations Of Lines

Example Question #13 : How To Find Slope Of A Line

Example Question #11 : How To Find Slope Of A Line

Example Question #12 : How To Find Slope Of A Line

Example Question #16 : How To Find Slope Of A Line

Example Question #17 : How To Find Slope Of A Line

Example Question #18 : How To Find Slope Of A Line

Example Question #11 : How To Find Slope Of A Line

Example Question #20 : How To Find Slope Of A Line

Example Question #21 : How To Find Slope Of A Line

All Algebra 1 Resources

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