### All Precalculus Resources

## Example Questions

### Example Question #1 : Linear Functions

**Possible Answers:**

**Correct answer:**

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

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

### Example Question #1 : Angles

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

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:**

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:**

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:**

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:**

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:**

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:**

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

.