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Algebra 1 : Slope and Line Equations

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Example Questions

Example Question #192 : Equations Of Lines

Find the slope of 10x+9y=8 .

Possible Answers:

$-\frac{4}{5}$

$\frac{10}{9}$

$-\frac{10}{9}$

Correct answer:

$-\frac{10}{9}$

Explanation:

Rewrite the equation in slope intercept form.

y=mx+b

Where represents the slope of the line and represents the -intercept.

10x+9y=8

9y=-10x+8

$y=-\frac{10}{9}x+8$

The slope is

$-\frac{10}{9}$ .

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Example Question #191 : Equations Of Lines

Given the points (2,3) and (4,6) .

Find the slope of the line.

Possible Answers:

$\frac{3}{2}$

$\frac{1}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

Use the given points and plug them into slope formula:

$m=\frac{\left ( y_{2}-y_{1} \right )}{(x_{2}-x_{1})}$

Remember points are written in the following format:

(x,y)

Substitute.

$m=\frac{6-3}{4-2}$

Simplify:

$m=\frac{3}{2}$

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Example Question #194 : Equations Of Lines

What is the slope of the line between points (0,4) and (2,2) ?

Possible Answers:

Correct answer:

Explanation:

The question asks for the slope of the line between two points.

*Always remember what the question is asking.

$Slope = m = rise/run = \frac{y_2-y_1}{x_2-x_1}$

Using coordinates

$(x_1, y_1)=({\color{Magenta} 0},{\color{DarkOrange} 4} ), (x_2,y_2)= ( 2,2)$ ,

and plugging them into the slope formula we get the following.

$\frac{2-{\color{DarkOrange} 4}}{2-{\color{Magenta} 0}} = \frac{-2}{2}= -1$

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Example Question #32 : How To Find Slope Of A Line

What is the slope of the equation $\frac{y-3x}{2}=4$ ?

Possible Answers:

-3/2

Correct answer:

Explanation:

The question is asking for the slope of the equation.

y=mx+b is the general form of an equation

"" is the slope of the equation, meaning how steep the line of the representing graph would be.

In order to find , you balance the equation to put it in the general format.

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

y-3x=8

$y={\color{Magenta} 3}x+8$

$m={\color{Magenta} 3}$

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Example Question #196 : Equations Of Lines

Find the slope of the line crossing through the points $\small (2,4) (10,7)$ .

Possible Answers:

$\small \frac{8}{3}$

$\small -\frac{3}{8}$

$\small -\frac{8}{3}$

$\frac{3}{8}$

Correct answer:

$\frac{3}{8}$

Explanation:

To find the slope of a line, all we need is the coordinates of two points that lie on the line. We are provided with two points in this problem.

The formula used is:

$\small \small \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

If we plug in the points provided:

$\small \small \frac{7-4}{10-2}= \frac{3}{8}$ .

Thus, our slope means that between these two points, we must rise 3 units and run 8 positive units.

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Example Question #191 : Equations Of Lines

What is the slope of the line that goes through the points $(-5, 1)\text{ and }(6, 2)$ ?

Possible Answers:

$-\frac{5}{3}$

$\frac{1}{11}$

$-\frac{11}{3}$

Correct answer:

$\frac{1}{11}$

Explanation:

The slope of a line is given by the following equation:

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

For the line in question,

$\text{Slope}=\frac{2-1}{6-(-5)}=\frac{1}{11}$

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Example Question #192 : Equations Of Lines

Find the slope of the line that goes through the following points: (-1, 1), (6, 0) .

Possible Answers:

$-\frac{1}{5}$

$\frac{1}{7}$

$-\frac{1}{7}$

Correct answer:

$-\frac{1}{7}$

Explanation:

The slope of a line is given by the following equation:

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

For the line in question,

$\text{Slope}=\frac{0-1}{6-(-1)}=-\frac{1}{7}$

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Example Question #193 : Equations Of Lines

Find the slope of the line that goes through the following points: (1, 1), (-2, -6)

Possible Answers:

$\frac{7}{3}$

$-\frac{7}{3}$

$-\frac{4}{7}$

Correct answer:

$\frac{7}{3}$

Explanation:

The slope of a line is given by the following equation:

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

For the line in question,

$\text{Slope}=\frac{-6-1}{-2-1}=\frac{-7}{-3}=\frac{7}{3}$

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Example Question #201 : Equations Of Lines

Find the slope of the line that goes through the following points: (10, 5), (-1, 0) .

Possible Answers:

$\frac{11}{5}$

$-\frac{1}{2}$

$\frac{5}{11}$

Correct answer:

$\frac{5}{11}$

Explanation:

The slope of a line is given by the following equation:

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

For the line in question,

$\text{Slope}=\frac{0-5}{-1-10}=\frac{-5}{-11}=\frac{5}{11}$

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Example Question #41 : How To Find Slope Of A Line

Find the slope of the line that goes through the following points: (5, 9), (1, -4) .

Possible Answers:

$\frac{4}{3}$

$-\frac{3}{4}$

$-\frac{10}{9}$

$\frac{13}{4}$

Correct answer:

$\frac{13}{4}$

Explanation:

The slope of a line is given by the following equation:

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

For the line in question,

$\text{Slope}=\frac{-4-9}{1-5}=\frac{-13}{-4}=\frac{13}{4}$

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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 #192 : Equations Of Lines

Example Question #191 : Equations Of Lines

Example Question #194 : Equations Of Lines

Example Question #32 : How To Find Slope Of A Line

Example Question #196 : Equations Of Lines

Example Question #191 : Equations Of Lines

Example Question #192 : Equations Of Lines

Example Question #193 : Equations Of Lines

Example Question #201 : Equations Of Lines

Example Question #41 : How To Find Slope Of A Line

All Algebra 1 Resources

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