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Algebra II : Graphing Linear Functions

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Example Question #1 : Graphing Linear Functions

Select the equation of the line perpendicular to the graph of 4y+3x=8 .

Possible Answers:

$y=-\frac{3}{4}x+8$

$y=\frac{3}{4}x-8$

$y=\frac{4}{3}x-7$

$y=-\frac{4}{3}x-7$

None of these.

Correct answer:

$y=\frac{4}{3}x-7$

Explanation:

Lines are perpendicular when their slopes are the negative recicprocals of each other such as $2\hspace{1mm}and\hspace{1mm}-\frac{1}{2}$ . To find the slope of our equation we must change it to slope y-intercept form.

4y+3x=8

Subtract the x variable from both sides:

4y=-3x+8

Divide by 4 to isolate y:

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

The negative reciprocal of the above slope: $\frac{-3}{4} \rightarrow \frac{4}{3}$ . The only equation with this slope is $y=\frac{4}{3}x-7$ .

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Example Question #11 : Graphing Linear Functions

Where does 6x-3y=9 cross the axis?

Possible Answers:

b=-3

b=6

b=-9

b=9

b=3

Correct answer:

b=-3

Explanation:

To find where this equation crosses the axis or its -intercept, change the equation into slope intercept form.

6x-3y=9

Subtract to isolate :

-3y=-6x+9

Divide both sides by to completely isolate :

y=2x-3

This form is the slope intercept form y=mx+b where is the slope of the line and is the -intercept.

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Example Question #12 : Graphing Linear Functions

Find the -intercepts and the -intercepts of the equation.

3x-4y=-24

Possible Answers:

(6,0) and (0,8)

(-8,0) and (0,-6)

(8,0) and (0,6)

(-8,0) and (0,6)

Correct answer:

(-8,0) and (0,6)

Explanation:

3x-4y=-24

To find the x-intercepts, remember that the line is crossing the x-axis, and that y=0 when the line crosses the x-axis.

So plug in y=0 into the equation above.

3x-4(0)=-24

3x=-24

x=-8

To find the y-intercepts, remember that the line is crossing the y-axis, and that x=0 when the line crosses the x-axis.

So plug in x=0 into the equation above.

3(0)-4y=-24

-4y=-24

y=6

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Example Question #13 : Graphing Linear Functions

Find the slope of the line that passes through the pair of points. Express the fraction in simplest form.

(-2,7) and (3,-1)

Possible Answers:

$\frac{5}{8}$

$-\frac{5}{8}$

$\frac{8}{5}{}$

$-\frac{8}{5}$

Correct answer:

$-\frac{8}{5}$

Explanation:

Slope is the change of a line. To find this line one can remember it as rise over run. This rise over run is really the change in the y direction over the change in the x direction.

Therefore the formula for slope is as follows.

$Slope = \frac{\Delta Y}{\Delta X}=\frac{y_2-y_1}{x_2-x_1}$

Plugging in our given points

(x_1,y_1)=(-2,7) and (x_2,y_2)=(3,-1)

$=\frac{-1-7}{3-(-2)}=\frac{-8}{5}$

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Example Question #14 : Graphing Linear Functions

Which of the following equations passes through (0,5) and is parallel to y=-6x+1 .

Possible Answers:

y=-6x+5

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

y=6x-5

$y=\frac{1}{6}$

Correct answer:

y=-6x+5

Explanation:

Since the line goes through (0,5) we know that (0,5) is the y-intercept.

Since we are looking for parallel lines, we need to write the equation of a line that has the same slope as the original, which is .

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

Therefore,

y=-6x+5 .

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Example Question #15 : Graphing Linear Functions

Write an equation of the line passing through (0,-3) and (4,1) in slope-intercept form.

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

Possible Answers:

y=-x-3

y=2x+1

y=x-3

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

Correct answer:

y=x-3

Explanation:

Step 1: Find the Slope

$Slope=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-1}{0-4}=\frac{-4}{-4}=1$

Step 2: Find the y-intercept

Use the slope and a point in the original y-intercept

y=mx+b

-3=1(0)+b

b=-3

Step 3: Write your equation

y=x-3

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Example Question #16 : Graphing Linear Functions

Find the slope-intercept form of an equation of the line that has a slope of $\frac{-3}{4}$ and passes through (8,2) .

Possible Answers:

$y=\frac{-3}{4}x-8$

$y=\frac{3}{4}x+8$

$y=\frac{-3}{4}x+8$

$y=\frac{4}{3}x+8$

Correct answer:

$y=\frac{-3}{4}x+8$

Explanation:

Since we know the slope and we know a point on the line we can use those two piece of information to find the y-intercept.

y=mx+b

$2=\frac{-3}{4}(8)+b$

2=-6+b

b=8

$y=\frac{-3}{4}x+8$

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Example Question #17 : Graphing Linear Functions

Determine the slope of a line that has points (2,3) and (-1,5) .

Possible Answers:

$\frac{2}{3}$

$-\frac{2}{3}$

$\frac{3}{2}$

$-\frac{3}{2}$

Correct answer:

$-\frac{2}{3}$

Explanation:

Slope is the change of a line. To find this line one can remember it as rise over run. This rise over run is really the change in the y direction over the change in the x direction.

Therefore the formula for slope is as follows.

$Slope = \frac{\Delta Y}{\Delta X}=\frac{y_2-y_1}{x_2-x_1}$

Plugging in our given points

(x_1,y_1)=(-1,5) and (x_2,y_2)=(2,3) ,

$Slope=\frac{y2-y1}{x2-x1}=\frac{5-3}{-1-2}=\frac{2}{-3}=-\frac{2}{3}$ .

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Example Question #18 : Graphing Linear Functions

What is the equation of the line passing through (-1,4) and (2,6)?

Possible Answers:

$y=\2x+\frac{14}{3}$

$y=-\frac{2}{3}x+\frac{14}{3}$

$y=\frac{2}{3}x+\frac{14}{3}$

$y=3x+\frac{14}{3}$

$y=\frac{2}{3}x-\frac{14}{3}$

Correct answer:

$y=\frac{2}{3}x+\frac{14}{3}$

Explanation:

To find the equation of this line, first find the slope. Recall that slope is the change in y over the change in x: $\frac{6-4}{2+1}=\frac{2}{3}$ . Then, pick a point and use the slope to plug into the point-slope formula ( $y-y_{1}=m(x-x_{1})$ ): $y-6=\frac{2}{3}(x-2)$ . Distribute and simplify so that you solve for y: $y=\frac{2}{3}x+\frac{14}{3}$ .

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Example Question #2 : Graphing Linear Functions

An individual's maximum heart rate can be found by subtracting his or her age from 220 . Which graph correctly expresses this relationship between years of age and maximum heart rate?

Possible Answers:

Screen_shot_2015-02-14_at_6.31.44_pm

Screen_shot_2015-02-14_at_6.24.06_pm

Screen_shot_2015-02-14_at_6.24.18_pm

Screen_shot_2015-02-14_at_6.24.40_pm

Screen_shot_2015-02-14_at_6.31.38_pm

Correct answer:

Screen_shot_2015-02-14_at_6.24.06_pm

Explanation:

In y=mx+b form, where y = maximum heart rate and x = age, we can express the relationship as:

y=-x+220

We are looking for a graph with a slope of -1 and a y-intercept of 220.

The slope is -1 because as you grow one year older, your maximum heart rate decreases by 1.

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Algebra II : Graphing Linear Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Graphing Linear Functions

Example Question #11 : Graphing Linear Functions

Example Question #12 : Graphing Linear Functions

Example Question #13 : Graphing Linear Functions

Example Question #14 : Graphing Linear Functions

Example Question #15 : Graphing Linear Functions

Example Question #16 : Graphing Linear Functions

Example Question #17 : Graphing Linear Functions

Example Question #18 : Graphing Linear Functions

Example Question #2 : Graphing Linear Functions

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