Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : How To Find The Slope Of A Tangent Line

What is the slope of the tangent line to the graph of  when ?

Possible Answers:

Correct answer:

Explanation:

To find the slope of the tangent line, first we must take the derivative of , giving us . Next we simply plug in our given x-value, which in this case is . This leaves us with a slope of .

Example Question #1501 : Intermediate Geometry

Suppose the equation of a line is .  What is the slope of the tangent line at ?

Possible Answers:

Correct answer:

Explanation:

Rewrite  in slope-intercept form, .

The slope of the tangent line is .

 

 

Example Question #1502 : Intermediate Geometry

Suppose a function .  What is the slope of the tangent line at ?

Possible Answers:

Correct answer:

Explanation:

Write the formula for slope-intercept form.

The slope of  is always zero at every point on the domain.  Therefore, the slope at  must also be zero.

Example Question #1 : How To Find X Or Y Intercept

Given the line what is the sum of the and intercepts?

Possible Answers:

Correct answer:

Explanation:

The intercepts cross an axis. 

For the intercept, set to get

For the intercept, set to get

So the sum of the intercepts is .

Example Question #3 : X And Y Intercept

What are the  and -intercepts of the line defined by the equation:

Possible Answers:

Correct answer:

Explanation:

To find the intercepts of a line, we must set the  and  values equal to zero and then solve.  

Example Question #2 : How To Find X Or Y Intercept

What is the -intercept of the following line:

Possible Answers:

Correct answer:

Explanation:

The -intercept is the point where the y-value is equal to 0. Therefore,

Example Question #3 : How To Find X Or Y Intercept

Which of the following statements regarding the x and y intercepts of the equation  is true?

Possible Answers:

The graph does not cross the y-axis.

The graph does not cross the x-axis.

The x and y intercepts are equal.

The x-intercept is greater than the y-intercept.

The y-intercept is greater than the x-intercept.

Correct answer:

The y-intercept is greater than the x-intercept.

Explanation:

To find the x-intercept, we simply plug  into our function. giving us . We can factor that equation, making it . We can not solve for , and we get . To find the y-intercept, we do the same thing, however this time, we plug in  instead. This leaves us with . With an x-intercept of  and a y-intercept of , it is clear that the y-intercept is greater than the x-intercept.

Example Question #3 : How To Find X Or Y Intercept

Find the -intercept of the following function.

Possible Answers:

DNE

Correct answer:

Explanation:

To find the x-intercept, set y equal to 0.

Now solve for x by dividing by 3 on both sides.

This reduces to,

Example Question #4 : How To Find X Or Y Intercept

Find the -intercept of the following function.

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept, set x equal to 0.

Now solve for y.

Example Question #3 : How To Find X Or Y Intercept

Which is the x-intercept for the line ?

Possible Answers:

Correct answer:

Explanation:

The x-intercept of a line is the x-value where the line hits the x-axis. This occurs when y is 0. To determine the x-value, plug in 0 for y in the original equation, then solve for x:

add 5 to both sides

divide by 2

Learning Tools by Varsity Tutors