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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : How To Find Slope Of A Line

$\textup{What is the slope of the linear equation }3y-4x=13\textup{ ?}$

Possible Answers:

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$-\frac{4}{3}$ $\displaystyle -\frac{4}{3}$

$-\frac{3}{4}$ $\displaystyle -\frac{3}{4}$

$\frac{13}{3}$ $\displaystyle \frac{13}{3}$

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

Correct answer:

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

Explanation:

$\textup{To find the slope, put the equation into }y=mx+b\textup{ format.}$

$\displaystyle 3y-4x=13$

$\displaystyle 3y=4x+13$

$y = \frac{4}{3}x+\frac{13}{3}\;\;\;\;\;\;\textup{slope}=m = \frac{4}{3}$

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Example Question #2 : How To Find Slope Of A Line

Which of the following is an example of an equation written in slope-intercept form?

Possible Answers:

-y=x-4 $\displaystyle -y=x-4$

y=-x+4 $\displaystyle y=-x+4$

y+x-4=0 $\displaystyle y+x-4=0$

y+x=4 $\displaystyle y+x=4$

Correct answer:

y=-x+4 $\displaystyle y=-x+4$

Explanation:

Slope intercept form is y=mx+b $\displaystyle y=mx+b$ , where $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept.

y=-x+4 $\displaystyle y=-x+4$ is the correct answer. The line has a slope of $\displaystyle -1$ and a y-intercept equal to $\displaystyle 4$ .

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Example Question #1 : How To Find Slope Of A Line

If (1,2) and (4,6) are on the same line, what is the slope of the line?

Possible Answers:

$\displaystyle 2$

$\displaystyle 1$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

Explanation:

$m=slope=\frac{\Delta y}{\Delta x}=\frac{\left ( y_{2}-y_{1}\right )}{\left ( x_{2}-x_{1}\right )}=$ $\displaystyle m=slope=\frac{\Delta y}{\Delta x}=\frac{\left ( y_{2}-y_{1}\right )}{\left ( x_{2}-x_{1}\right )}=$

$\frac{\left ( 6-2\right )}{\left ( 4-1\right )}=\frac{4}{3}$ $\displaystyle \frac{\left ( 6-2\right )}{\left ( 4-1\right )}=\frac{4}{3}$

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Example Question #1 : How To Find Slope Of A Line

The equation of a line is:

$\displaystyle 5x+25y=14$

What is the slope of the line?

Possible Answers:

$\frac{14}{25}$ $\displaystyle \frac{14}{25}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$-\frac{14}{25}$ $\displaystyle -\frac{14}{25}$

$-\frac{1}{5}$ $\displaystyle -\frac{1}{5}$

$\displaystyle 5$

Correct answer:

$-\frac{1}{5}$ $\displaystyle -\frac{1}{5}$

Explanation:

Solve the equation for y=mx+b $\displaystyle y=mx+b$

where $\displaystyle m$ is the slope of the line:

$\displaystyle 5x+25y=14$

$\displaystyle 25y=-5x+14$

$y=-\left ( \frac{5}{25} \right )x+\frac{14}{25}=-\left ( \frac{1}{5} \right )x+\frac{14}{25}$ $\displaystyle y=-\left ( \frac{5}{25} \right )x+\frac{14}{25}=-\left ( \frac{1}{5} \right )x+\frac{14}{25}$

$Slope=-\frac{1}{5}$ $\displaystyle Slope=-\frac{1}{5}$

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Example Question #3 : How To Find Slope Of A Line

A line passes through the points (-1,4) $\displaystyle (-1,4)$ and (4,-9) $\displaystyle (4,-9)$ . What is its slope?

Possible Answers:

$\frac{5}{13}$ $\displaystyle \frac{5}{13}$

$-\frac{13}{5}$ $\displaystyle -\frac{13}{5}$

- $-\frac{5}{13}$ $\displaystyle -\frac{5}{13}$

$\frac{13}{5}$ $\displaystyle \frac{13}{5}$

Correct answer:

$-\frac{13}{5}$ $\displaystyle -\frac{13}{5}$

Explanation:

The slope is the rise over the run. The line drops in $\displaystyle y$ -coordinates by 13 while gaining 5 in the $\displaystyle x$ -coordinates.

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Example Question #1 : How To Find Slope Of A Line

What is the slope of the line $\displaystyle 2y-4x=12$ ?

Possible Answers:

$\displaystyle 2$

$\displaystyle 6$

$\displaystyle 2$

$\displaystyle -4$

$\displaystyle 4$

Correct answer:

$\displaystyle 2$

Explanation:

You can rearrange $\displaystyle 2y-4x=12$ to get an equation resembling the y=mx+b $\displaystyle y=mx+b$ formula by isolating the $\displaystyle y$ . This gives you the equation y=2x+6 $\displaystyle y=2x+6$ . The slope of the equation is 2 (the $\displaystyle m$ within the y=mx+b $\displaystyle y=mx+b$ equation).

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Example Question #171 : Equations Of Lines

What is the slope of the line $\displaystyle 3y-9x=15$ ?

Possible Answers:

$\displaystyle 3$

$\displaystyle -9$

$\displaystyle 5$

$\displaystyle 9$

$\displaystyle -3$

Correct answer:

$\displaystyle 3$

Explanation:

To easily find the slope of the line, you can rearrange the equation to the y=mx+b $\displaystyle y=mx+b$ form. To do this, isolate the $\displaystyle y$ by moving the $\displaystyle x$ to the other side of the equation. This gives you $\displaystyle 3y=9x+15$ . Then, divide both sides by 3 to isolate the $\displaystyle y$ , which leaves you with y=3x+5 $\displaystyle y=3x+5$ . Now, the equation is in the y=mx+b $\displaystyle y=mx+b$ form, and you can easily see that the slope is 3.

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

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

$\displaystyle 6x+3y=15$

Possible Answers:

m=-2 $\displaystyle m=-2$

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

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

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

Correct answer:

m=-2 $\displaystyle m=-2$

Explanation:

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

$\displaystyle 6x+3y=15$

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

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

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

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Example Question #3701 : Algebra 1

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

Possible Answers:

$\displaystyle -24$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$-\frac{2}{3}$ $\displaystyle -\frac{2}{3}$

$-\frac{3}{2}$ $\displaystyle -\frac{3}{2}$

Correct answer:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Explanation:

$\displaystyle 4x - 6y = 15$

$\displaystyle -4x + 4x - 6y = -4x + 15$

$\displaystyle - 6y = -4x + 15$

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

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

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

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Example Question #3702 : Algebra 1

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

Possible Answers:

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\frac{6}{13}$ $\displaystyle \frac{6}{13}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\displaystyle 6$

Correct answer:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Explanation:

Use the slope formula:

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

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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 #3 : How To Find Slope Of A Line

Example Question #2 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #3 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #171 : Equations Of Lines

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

Example Question #3701 : Algebra 1

Example Question #3702 : Algebra 1

All Algebra 1 Resources

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