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Algebra 1 : Equations of Lines

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Example Question #161 : Equations Of Lines

A line passes through the points (3, 9) and (5, 3), and has a y-intercept of 3. Which of the following is an equation for that line?

Possible Answers:

y = 8x-12

$\small y = 9x-6$

$\small y = -4x + 8$

y = -2x-4

$\small \small y = -{3}x + 3$

Correct answer:

$\small \small y = -{3}x + 3$

Explanation:

The equation for a line is always $\small y = mx + b$ , where $\small m = slope$ and $\small b = y-intercept$ .

Given two data points, we are able to find the slope, m, using the formula

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

Using the data points provided, our formula will be:

$\small \small \frac{3-9}{5-3}$ , which gives us $\small \small -\frac{6}{2} ,$ or , $\small \small m = -3$ .

Our y-intercept is given.

Thus our equation for the line containing these points and that y-intercept is $\small \small y = -{3}x + 3$ .

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

What is the slope of the equation 4x + 3y = 7?

Possible Answers:

–4/3

3/4

–7/3

4/3

–3/4

Correct answer:

–4/3

Explanation:

We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4x + 3y = 7.

Isolate the y term: 3y = 7 – 4x

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

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

Find the slope of the line through the points (6,2) and (3,4).

Possible Answers:

$-\frac{2}{3}$

$-\frac{3}{2}$

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

$-\frac{2}{3}$

Explanation:

The equation for slope is $\frac{(y_2-y_1)}{(x_2-x_1)}$ . You plug in the coordinates from the points given you, and get $\frac{(4-2)}{(3-6)}$ , giving you $\frac{2}{-3}$ . Note that it does not matter which point you use as point 1 and point 2, as long as you are consistent.

$\frac{(y_2-y_1)}{(x_2-x_1)}$

(6,2) = (x₁,y₁)

(3,4) = (x₂,y₂)

$\frac{(4-2)}{(3-6)}=\frac{2}{-3}=-\frac{2}{3}$

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

Given the line 4y = 2x + 1, what is the slope of this line?

Possible Answers:

1/4

–2

1/2

–1/4

Correct answer:

1/2

Explanation:

4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.

4y = 2x + 1

(4y)/4 = (2x)/4 + (1)/4

y = 0.5x + 0.25

y = mx + b, where the slope is equal to m.

The coefficient is 0.5, so the slope is 1/2.

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

What is the slope of the line containing the points (7,12) and (91,32).

Possible Answers:

$\frac{44}{49}$

$\frac{51}{30}$

$\frac{5}{21}$

$\frac{3}{32}$

Correct answer:

$\frac{5}{21}$

Explanation:

To find the slope of a line you must first assign variables to each point. It does not matter which points get which variables as long as you keep the $x_{1}$ and $y_{1}$ and $x_{2}$ and $y_{2}$ consistent when you plug them into the equation.

Then we plug in the variables to this equation where represents the slope. $m=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$

Then we plug in our points for $x_{1},x_{2},y_{1},and\ y_{2}$ and the example looks like $m=\frac{(32-12)}{(91-7)}$

Then we perform the necessary subtraction and division to find an answer of $m=\frac{20}{84}=\frac{5}{21}$

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

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

Possible Answers:

$\frac{4}{3}$

$-\frac{3}{4}$

$\frac{13}{3}$

$\frac{3}{4}$

$-\frac{4}{3}$

Correct answer:

$\frac{4}{3}$

Explanation:

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

3y-4x=13

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

y+x=4

y+x-4=0

-y=x-4

Correct answer:

y=-x+4

Explanation:

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

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

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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:

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{1}{2}$

Correct answer:

$\frac{4}{3}$

Explanation:

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

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

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

The equation of a line is:

5x+25y=14

What is the slope of the line?

Possible Answers:

$\frac{14}{25}$

$-\frac{1}{5}$

$-\frac{14}{25}$

$\frac{1}{5}$

Correct answer:

$-\frac{1}{5}$

Explanation:

Solve the equation for y=mx+b

where is the slope of the line:

5x+25y=14

25y=-5x+14

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

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

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

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

Possible Answers:

$\frac{13}{5}$

$\frac{5}{13}$

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

$-\frac{13}{5}$

Correct answer:

$-\frac{13}{5}$

Explanation:

The slope is the rise over the run. The line drops in -coordinates by 13 while gaining 5 in the -coordinates.

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #161 : Equations Of Lines

Example Question #1 : 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 #2 : 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 #2 : How To Find Slope Of A Line

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