# Precalculus : Graph a Linear Function

## Example Questions

### Example Question #1 : Graph A Linear Function

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

Explanation:

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

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

Explanation:

For the linear function in point-slope form

The slope is equal to

For this problem

we get

### Example Question #51 : Graphing Functions

What is the y-intercept of the line below?

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 #52 : Graphing Functions

What is the slope of the line below?

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 #53 : Graphing Functions

What is the x-intercept of the equation below?