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Example Questions
Example Question #1501 : Intermediate Geometry
What is the slope of the tangent line to the graph of when
?
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 #11 : Tangent Lines
Suppose the equation of a line is . What is the slope of the tangent line at
?
Rewrite in slope-intercept form,
.
The slope of the tangent line is .
Example Question #221 : Coordinate Geometry
Suppose a function . What is the slope of the tangent line at
?
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?
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 #2 : How To Find X Or Y Intercept
What are the and
-intercepts of the line defined by the equation:
To find the intercepts of a line, we must set the and
values equal to zero and then solve.
Example Question #1 : How To Find X Or Y Intercept
What is the -intercept of the following line:
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?
The x-intercept is greater than the y-intercept.
The graph does not cross the y-axis.
The y-intercept is greater than the x-intercept.
The x and y intercepts are equal.
The graph does not cross the x-axis.
The y-intercept is greater than the x-intercept.
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 #2 : How To Find X Or Y Intercept
Find the -intercept of the following function.
DNE
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 #3 : How To Find X Or Y Intercept
Find the -intercept of the following function.
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 ?
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
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