Precalculus : Graph a Linear Function

Example Questions

Example Question #1 : Linear Functions

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 #5 : Linear Functions

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 #6 : Linear Functions

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 #7 : Linear 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 #1 : Graph A Linear Function

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 #9 : Linear Functions

What is the x-intercept of the equation below?       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 All Precalculus Resources 