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Algebra 1 : Functions and Lines

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Example Questions

Example Question #4 : How To Find The Equation Of A Line

Given two points $\left ( 1,5 \right )$ and $\left ( 0,2 \right )$ , find the equation of a line that passes through the point $\left ( -3,-5 \right )$ and is parallel to the line passing through points and .

Possible Answers:

x-3y=-4

x-3y=-12

2x+2y=6

3x-y=-4

3x-y=4

Correct answer:

3x-y=-4

Explanation:

The slope of the line passing through points and can be computed as follows:

$Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{5-2}{1-0}=3$

Now, the new line, since it is parallel, will have the same slope. To find the equation of this new line, we use point-slope form:

$y-y_{1}=m(x-x_{1})$ , where is the slope and $\left ( x_{1},y_{1} \right )$ is the point the line passes through.

y-(-5)=3(x-(-3))

y+5-3(x+3)

y+5=3x+9

After rearranging, this becomes 3x-y=-4

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

Find the equation, in y=mx+b form, of the line that contains the points (2,10) and (-4,13) .

Possible Answers:

y=2x+6

y=11x-5

y=-2x+5

$y=\frac{1}{2}x+9$

$y=-\frac{1}{2}x+11$

Correct answer:

$y=-\frac{1}{2}x+11$

Explanation:

When finding the equation of a line from some of its points, it's easiest to first find the line's slope, or .

To find slope, divide the difference in values by the difference in values. This gives us divided by , or $-\frac{1}{2}$ .

Next, we just need to find , which is the line's -intercept. By plugging one of the points into the equation $y = -\frac{1}{2}x+b$ , we obtain a value of 11 and a final equation of

$y=-\frac{1}{2}x+11$

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Example Question #2 : How To Find The Equation Of A Line

What is the equation of a straight line that connects the points indicated in the table?

Possible Answers:

y=4x+3

y=2x+6

y=x+6

y=3x+4

Correct answer:

y=3x+4

Explanation:

We can find the equation of th line in slope-intercept form by finding and .

First, calculate the slope, , for any two points. We will use the first two.

$m=\frac{y_{2}-y_1}{x_2-x_1}=\frac{7-4}{1-0}=\frac{3}{1}=3$

Next, using the slope and any point on the line, calculate the y-intercept, . We will use the first point.

y=mx+b

4=3(0)+b

4=b

The correct equation in slope-intercept form is y=3x+4 .

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

What is the equation of a line with a slope of and a -intercept of ?

Possible Answers:

None of the above

y=-12x+2

y=2x+12

y=2x-12

y=x+6

Correct answer:

y=2x-12

Explanation:

When a line is in the y=mx+b format, the is its slope and the is its -intercept. In this case, the equation with a slope of and a -intercept of is y=2x-12 .

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Example Question #5 : How To Find The Equation Of A Line

In 1990, the value of a share of stock in General Vortex was $27.17. In 2000, the value was $48.93. If the value of the stock rose at a generally linear rate between those two years, which of the following equations most closely models the price of the stock, , as a function of the year, ?

Possible Answers:

p(x)=2.176x-4,303.07

p(x)=2.176x-4,400.93

p(x)=-2.176x+4,400.93

p(x)=-2.176x+4,303.07

p(x)=2.176x-2,106.47

Correct answer:

p(x)=2.176x-4,303.07

Explanation:

We can treat the price of the stock as the value and the year as the value, making any points take the form (year, price) , or (x,p) . This question is asking for the line that includes points (1990,27.17) and (2000,48.93) .

To find the equation, first, we need the slope.

$m= \frac{48.93-27.17}{2000-1990}= \frac{21.76}{10}=2.176$

Now use the point-slope formula with this slope and either point (we will choose the second).

y-48.93 = 2.176(x-2000)

y-48.93 = 2.176x-4352

y = 2.176x-4303.07

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Example Question #6 : 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=-2x+1

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

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

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 #7 : 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=5x+6

y=x+5

y=6x+5

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

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 : Slope And Line Equations

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

Possible Answers:

y=-6x+4

None of the other answers

y=4x-6

y=4x+6

y=2x-3

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

None of the other answers

y=3x-3

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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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #4 : How To Find The Equation Of A Line

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

Example Question #2 : How To Find The Equation Of A Line

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

Example Question #5 : How To Find The Equation Of A Line

Example Question #6 : How To Find The Equation Of A Line

Example Question #7 : How To Find The Equation Of A Line

Example Question #11 : Slope And Line Equations

Example Question #12 : Slope And Line Equations

Example Question #13 : Slope And Line Equations

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