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Algebra 1 : Functions and Lines

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Example Questions

Example Question #421 : Functions And Lines

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

Possible Answers:

$\frac{13}{6}$

$\frac{1}{10}$

$-\frac{1}{2}$

$\frac{6}{13}$

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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Example Question #421 : Functions And Lines

Find the slope of the line that passes through the points (0,2) and (5,-2).

Possible Answers:

0.80

-0.80

-0.50

Correct answer:

-0.80

Explanation:

To find the slope of the line passing through the given points, we need to find the change in y and divide it by the change in x. This can also be written as $\frac{y_{1}-y_0}{x_1-x_0}$ . In our case, we have $\frac{-2-2}{5-0}=\frac{-4}{5}=-0.80$

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Example Question #23 : How To Find Slope Of A Line

Find the slope of the line using the following given points:

(2,5), (5,6), (8,7)

Possible Answers:

$\frac{1}{3}$

$-\frac{1}{3}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{3}$

Explanation:

To find the slope, divide the change in by the change in .

So,

$\frac{6-5}{5-2}=\frac{1}{3}$

Check your answer by using the same equation on another pair of points:

$\frac{7-6}{8-5}=\frac{1}{3}$

It's the same! So the answer is $\frac{1}{3}$ .

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Example Question #24 : How To Find Slope Of A Line

What is the y-intercept of the line

$6y-3x=9\ ?$

Possible Answers:

$\frac{3}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

To easily determine an equation's y-intercept, convert it to the y=mx+b form, where the represents the equation's y-intercept.

Converting the given equation to this form gives you

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

with a y-intercept of $\frac{3}{2}$ .

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #421 : Functions And Lines

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

Example Question #421 : Functions And Lines

Example Question #23 : How To Find Slope Of A Line

Example Question #24 : How To Find Slope Of A Line

All Algebra 1 Resources

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