Precalculus : Linear Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Linear Functions

Solve for .

Question_2

(Figure not drawn to scale).

Possible Answers:

Correct answer:

Explanation:

The angles are supplementary, therefore, the sum of the angles must equal .

Example Question #1 : Graphing Functions

Are  and  supplementary angles?

Possible Answers:

No

Not enough information

Yes

Correct answer:

Yes

Explanation:

Since supplementary angles must add up to , the given angles are indeed supplementary.

Example Question #1 : Angles

Solve for and .

Question_3

(Figure not drawn to scale).

Possible Answers:

Correct answer:

Explanation:

The angles containing the variable  all reside along one line, therefore, their sum must be .

Because  and  are opposite angles, they must be equal.

Example Question #1 : Linear Functions

Which of the following could be the function modeled by this graph?

Linearfxn

Possible Answers:

Correct answer:

Explanation:

Which of the following could be the function modeled by this graph?

Linearfxn

We can begin here by trying to identify a couple points  on the graph

We can see that it crosses the y-axis at 

Therefore, not only do we have a point, we have the y-intercept. This tells us that the equation of the line needs to have a  in it somewhere. Eliminate any option that do not have this feature.

Next, find the slope by counting up and over from the y-intercept to the next clear point.

It seems like the line goes up 5 and right 1 to the point 

This means we have a slope of 5, which means our equation must look like this:

 

Example Question #2 : Graph A Linear Function

Find the slope of the linear function

Possible Answers:

Correct answer:

Explanation:

For the linear function in point-slope form

The slope is equal to 

For this problem

we get

Example Question #3 : Graph A Linear Function

Find the slope of the linear function

Possible Answers:

Correct answer:

Explanation:

For the linear function in point-slope form

The slope is equal to 

For this problem

we get

Example Question #1 : Linear Functions

What is the y-intercept of the line below? 

Possible Answers:

Correct answer:

Explanation:

By definition, the y-intercept is the point on the line that crosses the y-axis. This can be found by substituting  into the equation. When we do this with our equation, 

Alternatively, you can remember  form, a general form for a line in which  is the slope and  is the y-intercept. 

Example Question #1 : Linear Functions

What is the slope of the line below? 

Possible Answers:

Correct answer:

Explanation:

Recall slope-intercept form, or . In this form,  is the slope and  is the y-intercept. Given our equation above, the slope must be the coefficient of the x, which is 

Example Question #6 : Graph A Linear Function

What is the x-intercept of the equation below? 

Possible Answers:

Correct answer:

Explanation:

The x-intercept of an equation is the point at which the line crosses the x-axis. Thus, we can find the x-intercept by plugging in . When we do this with our equation: 

Thus, our x-intercept is the point 

Example Question #1 : Determine The Equation Of A Linear Function

What is the equation of the line that passes through the points  and ?

Express your answer in  form.

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

First, we need to compute , the slope. We can do this with the slope formula

, sometimes called "rise over run"

 So we now have

Now in order to solve for  we substitute one of our points into the equation we found. It doesn't matter which point we use, so we'll use .

We then have:

Which becomes .

Hence we take our found value for  and plug it back into  to get

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