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Algebra 1 : Equations of Lines

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Example Questions

Example Question #1 : How To Find The Equation Of A Line

$\textup{What is the equation of the line in the }xy\textup{-coordinate plane that}$

$\textup{passes through the points }\left ( -6,4\right )\textup{and}\left ( -2,2\right )?$

Possible Answers:

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

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

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

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

y=-2x+1

Correct answer:

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

Explanation:

$\textup{Equation of a line is }y=mx+b \textup{, where }m\textup{ is the slope and }b\textup{ is the }y\textup{-intercept.}$

$\textup{Find slope} = \frac{\Delta y}{\Delta x}=\frac{2-4}{-2--6}=\frac{-2}{4}=\frac{-1}{2}$

$\textup{Use slope to find }y\textup{-intercept:} \frac{-1}{2}= \frac{b-2}{0--2}\;\;\;\;\frac{-1}{2}=\frac{b-2}{2}$

$2b-4 = -2\;\;\;\;\;\;2b = 2\;\;\;\;\;b=1$

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

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Example Question #1 : How To Find The Equation Of A Line

Which of these lines has a slope of 5 and a -intercept of 6?

Possible Answers:

y=6x+5

y=-5x-6

$y=\frac{1}{5}x+6$

y=x+5

y=5x+6

Correct answer:

y=5x+6

Explanation:

When an equation is in the y=mx+b form, the indicates its slope while the indicates its -intercept. In this case, we are looking for a line with a of 5 and a of 6, or y=5x+6 .

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Example Question #11 : How To Find The Equation Of A Line

Which of these lines has a slope of and a -intercept of ?

Possible Answers:

None of the other answers

y=-6x+4

y=4x-6

y=2x-3

y=4x+6

Correct answer:

y=4x-6

Explanation:

When a line is in the y=mx+b form, the is its slope and the is its -intercept. Thus, the only line with a slope of and a -intercept of is

y=4x-6 .

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Example Question #12 : Slope And Line Equations

What is the equation of a line with a slope of 3 that runs through the point (4,9)?

Possible Answers:

y=3x+3

y=3x-3

None of the other answers

y=-3x-3

y=-3x+3

Correct answer:

y=3x-3

Explanation:

You can find the equation by plugging in all of the information to the y=mx+b formula.

The slope (or ) is 3. So, the equation is now y=3x+b .

You are also given a point on the line: (4,9), which you can plug into the equation:

9=3(4)+b

Solve for to get b=-3 .

Now that you have the and , you can determine that the equation of the line is y=3x-3 .

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Example Question #13 : Slope And Line Equations

What is the equation of the line passing through the points (1,2) and (3,1) ?

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

First find the slope of the 2 points:

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

Then use the slope and one of the points to find the y-intercept:

$2=\frac{-1}{2}(1)+b$

$\frac{4}{2}+\frac{1}{2}=-\frac{1}{2}+\frac{1}{2}+b$

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

So the final equation is $y=-\frac{1}{2}x+\frac{5}{2}$

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Example Question #14 : Slope And Line Equations

What is the slope and y-intercept of 2y-4x=12 ?

Possible Answers:

Slope: ; y-intercept:

None of the other answers

Slope: ; y-intercept:

Correct answer:

Slope: ; y-intercept:

Explanation:

The easiest way to determine the slope and y-intercept of a line is by rearranging its equation to the y=mx+b form. In this form, the slope is the and the y-intercept is the .

Rearranging 2y-4x=12

gives you

y=2x+6

which has an of 2 and a of 6.

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Example Question #101 : Equations Of Lines

Find the equation of the line, in y=mx+b form, that contains the points (1,6) , (11,12) , and (-9,0) .

Possible Answers:

y = 3x +5

y = 10x - 4

$y=\frac{3}{5}x +\frac{27}{5}$

$y = \frac{3}{5}x - 7$

$y = \frac{5}{3}x + \frac{13}{3}$

Correct answer:

$y=\frac{3}{5}x +\frac{27}{5}$

Explanation:

When finding the equation of a line given two or more points, the first step is to find the slope of that line. We can use the slope equation, $\frac{y_{2}-y_{_{1}}}{x_{2}-x_{1}}$ . Any combination of the three points can be used, but let's consider the first two points, (1,6) and (11,12) .

$\frac{12-6}{11-1} = \frac{3}{5}$

So $\frac{3}{5}$ is our slope.

Now, we have the half-finished equation

$y = \frac{3}{5}x + b$

and we can complete it by plugging in the and values of any point. Let's use (1,6) .

Solving

$6 = \frac{3}{5}(1)+b$

for gives us

$b = 6 - \frac{3}{5}$

$b = 5\frac{2}{5} = \frac{27}{5}$

We now have our completed equation:

$y = \frac{3}{5}x + \frac{27}{5}$

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Example Question #16 : Slope And Line Equations

We have two points: (-3,-1) and (4,9) .

If these two points are connected by a straight line, find the equation describing this straight line.

Possible Answers:

$y=\frac{10}{3}x+\frac{3}{7}$

$y=\frac{10}{7}x+\frac{23}{7}$

None of these

$y=\frac{9}{2}x-\frac{3}{2}$

$y=-\frac{10}{3}x+\frac{3}{7}$

Correct answer:

$y=\frac{10}{7}x+\frac{23}{7}$

Explanation:

We need to find the equation of the line in slope-intercept form.

y=mx+b

In this formula, is equal to the slope and is equal to the y-intercept.

To find this equation, first, we need to find the slope by using the formula for the slope between two point.

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

In the formula, the points are and . In our case, the points are (-3,-1) and (4,9) . Using our values allows us to solve for the slope.

$m=\frac{9-(-1)}{4-(-3)}=\frac{10}{7}$

We can replace the variable with our new slope.

$y=\frac{10}{7}x+b$

Next, we need to find the y-intercept. To find this intercept, we can pick one of our given points and use it in the formula.

(-3,-1)

$-1=\frac{10}{7}(-3)+b$

Solve for .

$-1=\frac{-30}{7}+b$

$b=-1+\frac{30}{7}$

$b=\frac{23}{7}$

Now, the final equation connecting the two points can be written using the new value for the y-intercept.

$y=\frac{10}{7}x+\frac{23}{7}$

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Example Question #17 : Slope And Line Equations

Which of these lines has a slope of and a y-intercept of ?

Possible Answers:

y=3x-4

y=-4x+3

y=4x-3

None of the other answers

y=-3x+4

Correct answer:

y=-3x+4

Explanation:

Since all of the answers are in the y=mx+b form, the slope of each line is indicated by its and its y-intercept is indicated by its . Thus, a line with a slope of and a y-intercept of must have an equation of y=-3x+4 .

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Example Question #18 : Slope And Line Equations

Find the domain of:

$\sqrt{2x-5}$

Possible Answers:

$\left \{ x|x\neq \frac{5}{2} \right \}$

$\left \{ x|x\geq \frac{5}{2} \right \}$

$\left \{ x|-\infty < x< \infty \right \}$

$\left \{ x|x\leq \frac{5}{2} \right \}$

$\left \{ x|x= \frac{5}{2} \right \}$

Correct answer:

$\left \{ x|x\geq \frac{5}{2} \right \}$

Explanation:

The expression under the radical must be $\geq 0$ . Hence

$\sqrt{2x-5} \geq 0$

Solving for , we get

$x\geq \frac{5}{2}$

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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 #1 : How To Find The Equation Of A Line

Example Question #1 : How To Find The Equation Of A Line

Example Question #11 : How To Find The Equation Of A Line

Example Question #12 : Slope And Line Equations

Example Question #13 : Slope And Line Equations

Example Question #14 : Slope And Line Equations

Example Question #101 : Equations Of Lines

Example Question #16 : Slope And Line Equations

Example Question #17 : Slope And Line Equations

Example Question #18 : Slope And Line Equations

All Algebra 1 Resources

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