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Example Questions
Example Question #1 : Slope Intercept Form
Which of the following equations is written in slope-intercept form?
Slope-intercept form is written as .
There is only one answer choice in this form:
Example Question #1 : Slope Intercept Form
Rewrite the following equation in slope-intercept form.
The slope-intercept form of a line is: , where
is the slope and
is the y intercept.
Below are the steps to get the equation into slope-intercept form.
Example Question #1 : Linear Algebra
Refer to the above red line. What is its equation in slope-intercept form?
First, we need to find the slope of the above line.
Given two points, , the slope can be calculated using the following formula:
Set :
Second, we note that the -intercept is the point
.
Therefore, in the slope-intercept form of a line, we can set and
:
Example Question #4 : Slope Intercept Form
What is the y-intercept of the line with the following equation:
There are two ways that you can find the y-intercept for an equation. You could substitute in for
. This would give you:
Simplifying, you get:
However, another way to do this is by finding the slope-intercept form of the line. You do this by solving for :
Just divide everything by :
Remember that the slope-intercept form gives you the intercept as the final constant. Hence, it is as well!
Example Question #5 : Slope Intercept Form
What is the y-intercept for the following equation:
There are two ways that you can find the y-intercept for an equation. You could substitute in for
. This would give you:
Simplifying, you get:
However, another way to do this is by finding the slope-intercept form of the line. You do this by solving for . Indeed, this is very, very easy. Recall that the slope intercept form is:
This means that, as written, your equation obviously has . You don't even have to do all of the simplification!
Example Question #6 : Slope Intercept Form
What is the equation of the line between and
?
In order to figure this out, you should use your slope-intercept formula. Remember that the y-intercept is the place where is zero. Therefore, the point
gives you your y-intercept. It is
. Now, to find the slope, recall the slope equation, namely:
For your points, this would be:
This is your slope.
Now, recall that the point-slope form of an equation is:
, where
is your slope and
is your y-intercept
Thus, your equation will be:
Example Question #7 : Slope Intercept Form
Which of the following equations has a slope of ?
In order to compute the slope of a line, there are several tools you can use. For this question, try to use the slope-intercept form of a line. Once you get the equation into this form, you basically can "read off" the slope right from the equation! Recall that the slope-intercept form of an equation is:
Now, looking at each of your options, you know that you can eliminate two immediately, as their slopes obviously are not :
The next is almost as easy:
When you solve for , your coefficient value for
is definitely not equal to
:
Next, is not correct either. When you start to solve, you should notice that
will always have a negative coefficient. This means that it certainly will not become
when you finish out the simplification.
Thus, the correct answer is:
Really, all you have to pay attention to is the term. First, you will subtract
from both sides:
Then, just divide by , and you will have
!
Example Question #2 : Linear Algebra
Rewrite the equation in slope-intercept form:
In order to rewrite the equation in slope-intercept form, we will need to multiply the reciprocal of the coefficient in front of y.
Simplify both sides.
The answer is:
Example Question #9 : Slope Intercept Form
Write the equation in slope-intercept form:
The slope-intercept form is:
Subtract on both sides.
Divide by negative six on both sides.
Simplify both sides.
The answer is:
Example Question #1 : Linear Algebra
Write the equation in slope-intercept form:
Slope intercept form is .
Add on both sides.
Multiply by three on both sides.
The answer is:
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