Precalculus : Graph a Linear Function

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1119 : Pre Calculus

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 #1 : 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 #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

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 #1123 : Pre Calculus

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 #1124 : Pre Calculus

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 

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