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Example Questions
Example Question #1 : How To Find The Equation Of A Line
Given two points and
, find the equation for the line connecting those two points in slope-intercept form.
If we have two points, we can find the slope of the line between them by using the definition of the slope:
where the triangle is the greek letter 'Delta', and is used as a symbol for 'difference' or 'change in'
Now that we have our slope ( , simplified to
), we can write the equation for slope-intercept form:
where
is the slope and
is the y-intercept
In order to find the y-intercept, we simply plug in one of the points on our line
So our equation looks like
Example Question #1 : How To Find The Equation Of A Line
Which of the following is an equation for a line with a slope of and a y-intercept of
?
Because we have the desired slope and the y-intercept, we can easily write this as an equation in slope-intercept form (y=mx+b).
This gives us . Because this does not match either of the answers in this form (y=mx+b), we must solve the equation for x. Adding 5 to each side gives us
. We can then multiple both sides by 3 and divide both sides by 4, giving us
.
Example Question #3 : How To Find The Equation Of A Line
If the -intercept of a line is
, and the
-intercept is
, what is the equation of this line?
If the y-intercept of a line is , then the
-value is
when
is zero. Write the point:
If the -intercept of a line is
, then the
-value is
when
is zero. Write the point:
Use the following formula for slope and the two points to determine the slope:
Use the slope intercept form and one of the points, suppose , to find the equation of the line by substituting in the values of the point and solving for
, the
-intercept.
Therefore, the equation of this line is .
Example Question #4 : How To Find The Equation Of A Line
What is the equation of a line that has a slope of and a
-intercept of
?
The slope intercept form can be written as:
where is the slope and
is the y-intercept. Plug in the values of the slope and
-intercept into the equation.
The correct answer is:
Example Question #5 : How To Find The Equation Of A Line
What is the equation of a line with a slope of and an
-intercept of
?
The -intercept is the value of
when the
value is equal to zero. The actual point located on the graph for an
-intercept of
is
. The slope,
, is 2.
Write the slope-intercept equation and substitute the point and slope to solve for the -intercept:
Plug the slope and -intercept back in the slope-intercept formula:
Example Question #6 : How To Find The Equation Of A Line
A line goes through the following points and
.
Find the equation of the line.
First, find the slope of the line using the slope formula:
.
Next we plug one of the points, and the slope, into the point-intercept line forumula:
where m is our slope.
Then and when we plug in point (2,3) the formula reads
then solve for b.
.
To find the equation of the line, we plug in our m and b into the slope-intercept equation.
So, or simplified,
.
Example Question #1 : How To Find The Equation Of A Line
Write the equation for the line passing through the points and
To determine the equation, first find the slope:
We want this equation in slope-intercept form, . We know
and
because we have two coordinate pairs to choose from representing an
and a
. We know
because that represents the slope. We just need to solve for
, and then we can write the equation.
We can choose either point and get the correct answer. Let's choose :
multiply "
"
add
to both sides
This means that the form is
Example Question #8 : How To Find The Equation Of A Line
Write the equation for a line that passes through the points and
.
To determine the equation, first find the slope:
We want this equation in slope-intercept form, . We know
and
because we have two coordinate pairs to choose from representing an
and a
. We know
because that represents the slope. We just need to solve for
, and then we can write the equation.
We can choose either point and get the correct answer. Let's choose :
multiply "
"
subtract
from both sides
This means that the form is
Example Question #9 : How To Find The Equation Of A Line
Find the equation for a line passing through the points and
.
To determine the equation, first find the slope:
We want this equation in slope-intercept form, . We know
and
because we have two coordinate pairs to choose from representing an
and a
. We know
because that represents the slope. We just need to solve for
, and then we can write the equation.
We can choose either point and get the correct answer. Let's choose :
multiply "
"
subtract
from both sides
This means that the form is
Example Question #10 : How To Find The Equation Of A Line
Find the equation for the line passing through the points and
.
To determine the equation, first find the slope:
We want this equation in slope-intercept form, . We know
and
because we have two coordinate pairs to choose from representing an
and a
. We know
because that represents the slope. We just need to solve for
, and then we can write the equation.
We can choose either point and get the correct answer. Let's choose :
multiply "
"
subtract
from both sides
This means that the form is
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