Graph a Linear Function - Pre-Calculus

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:

For the linear function in point-slope form

The slope is equal to

For this problem

we get

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.

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 .

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 .

For the linear function in point-slope form

The slope is equal to

For this problem

we get

For the linear function in point-slope form

The slope is equal to

For this problem

we get

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:

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.

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 .

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 .

For the linear function in point-slope form

The slope is equal to

For this problem

we get

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:

For the linear function in point-slope form

The slope is equal to

For this problem

we get

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.

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 .

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 .

For the linear function in point-slope form

The slope is equal to

For this problem

we get

For the linear function in point-slope form

The slope is equal to

For this problem

we get