All Intermediate Geometry Resources
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 ?
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 ?
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 ?
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 #3 : X And 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 #2 : 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 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.
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 #3 : 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 #4 : 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