Calculating the equation of a line - GMAT Quantitative
Card 0 of 56
Find the equation of the line through the points
and
.
Find the equation of the line through the points and
.
First find the slope of the equation.

Now plug in one of the two points to form an equation. Here we use (4, -2), but either point will produce the same answer.



First find the slope of the equation.
Now plug in one of the two points to form an equation. Here we use (4, -2), but either point will produce the same answer.
Compare your answer with the correct one above
What is the equation of a line with slope
and a point
?
What is the equation of a line with slope and a point
?
Since the slope and a point on the line are given, we can use the point-slope formula:






Since the slope and a point on the line are given, we can use the point-slope formula:
Compare your answer with the correct one above
What is the equation of a line with slope
and point
?
What is the equation of a line with slope and point
?
Since the slope and a point on the line are given, we can use the point-slope formula:





Since the slope and a point on the line are given, we can use the point-slope formula:
Compare your answer with the correct one above
What is the equation of a line with slope
and a point
?
What is the equation of a line with slope and a point
?
Since the slope and a point on the line are given, we can use the point-slope formula:

slope:
and point: 






Since the slope and a point on the line are given, we can use the point-slope formula:
slope: and point:
Compare your answer with the correct one above
Consider segment
which passes through the points
and
.
Find the equation of
in the form
.
Consider segment which passes through the points
and
.
Find the equation of in the form
.
Given that JK passes through (4,5) and (144,75) we can find the slope as follows:
Slope is found via:

Plug in and calculate:

Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).


So our answer is:

Given that JK passes through (4,5) and (144,75) we can find the slope as follows:
Slope is found via:
Plug in and calculate:
Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).
So our answer is:
Compare your answer with the correct one above
Determine the equation of a line that has the points
and
?
Determine the equation of a line that has the points and
?
The equation for a line in standard form is written as follows:

Where
is the slope and
is the y intercept. We start by calculating the slope between the two given points using the following formula:

Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:



We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:

The equation for a line in standard form is written as follows:
Where is the slope and
is the y intercept. We start by calculating the slope between the two given points using the following formula:
Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:
We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:
Compare your answer with the correct one above
Give the equation of the line that passes through the
-intercept and the vertex of the parabola of the equation
.
Give the equation of the line that passes through the -intercept and the vertex of the parabola of the equation
.
The
-intercept of the parabola of the equation can be found by substituting 0 for
:



This point is
.
The vertex of the parabola of the equation
has
-coordinate
, and its
-coordinate can be found using substitution for
. Setting
and
:





The vertex is 
The line connects the points
and
. Its slope is






Since the line has
-intercept
and slope
, the equation of the line is
, or
.
The -intercept of the parabola of the equation can be found by substituting 0 for
:
This point is .
The vertex of the parabola of the equation has
-coordinate
, and its
-coordinate can be found using substitution for
. Setting
and
:
The vertex is
The line connects the points and
. Its slope is
Since the line has -intercept
and slope
, the equation of the line is
, or
.
Compare your answer with the correct one above
Find the equation of the line through the points
and
.
Find the equation of the line through the points and
.
First find the slope of the equation.

Now plug in one of the two points to form an equation. Here we use (4, -2), but either point will produce the same answer.



First find the slope of the equation.
Now plug in one of the two points to form an equation. Here we use (4, -2), but either point will produce the same answer.
Compare your answer with the correct one above
What is the equation of a line with slope
and a point
?
What is the equation of a line with slope and a point
?
Since the slope and a point on the line are given, we can use the point-slope formula:






Since the slope and a point on the line are given, we can use the point-slope formula:
Compare your answer with the correct one above
What is the equation of a line with slope
and point
?
What is the equation of a line with slope and point
?
Since the slope and a point on the line are given, we can use the point-slope formula:





Since the slope and a point on the line are given, we can use the point-slope formula:
Compare your answer with the correct one above
What is the equation of a line with slope
and a point
?
What is the equation of a line with slope and a point
?
Since the slope and a point on the line are given, we can use the point-slope formula:

slope:
and point: 






Since the slope and a point on the line are given, we can use the point-slope formula:
slope: and point:
Compare your answer with the correct one above
Consider segment
which passes through the points
and
.
Find the equation of
in the form
.
Consider segment which passes through the points
and
.
Find the equation of in the form
.
Given that JK passes through (4,5) and (144,75) we can find the slope as follows:
Slope is found via:

Plug in and calculate:

Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).


So our answer is:

Given that JK passes through (4,5) and (144,75) we can find the slope as follows:
Slope is found via:
Plug in and calculate:
Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).
So our answer is:
Compare your answer with the correct one above
Determine the equation of a line that has the points
and
?
Determine the equation of a line that has the points and
?
The equation for a line in standard form is written as follows:

Where
is the slope and
is the y intercept. We start by calculating the slope between the two given points using the following formula:

Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:



We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:

The equation for a line in standard form is written as follows:
Where is the slope and
is the y intercept. We start by calculating the slope between the two given points using the following formula:
Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:
We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:
Compare your answer with the correct one above
Give the equation of the line that passes through the
-intercept and the vertex of the parabola of the equation
.
Give the equation of the line that passes through the -intercept and the vertex of the parabola of the equation
.
The
-intercept of the parabola of the equation can be found by substituting 0 for
:



This point is
.
The vertex of the parabola of the equation
has
-coordinate
, and its
-coordinate can be found using substitution for
. Setting
and
:





The vertex is 
The line connects the points
and
. Its slope is






Since the line has
-intercept
and slope
, the equation of the line is
, or
.
The -intercept of the parabola of the equation can be found by substituting 0 for
:
This point is .
The vertex of the parabola of the equation has
-coordinate
, and its
-coordinate can be found using substitution for
. Setting
and
:
The vertex is
The line connects the points and
. Its slope is
Since the line has -intercept
and slope
, the equation of the line is
, or
.
Compare your answer with the correct one above
Find the equation of the line through the points
and
.
Find the equation of the line through the points and
.
First find the slope of the equation.

Now plug in one of the two points to form an equation. Here we use (4, -2), but either point will produce the same answer.



First find the slope of the equation.
Now plug in one of the two points to form an equation. Here we use (4, -2), but either point will produce the same answer.
Compare your answer with the correct one above
What is the equation of a line with slope
and a point
?
What is the equation of a line with slope and a point
?
Since the slope and a point on the line are given, we can use the point-slope formula:






Since the slope and a point on the line are given, we can use the point-slope formula:
Compare your answer with the correct one above
What is the equation of a line with slope
and point
?
What is the equation of a line with slope and point
?
Since the slope and a point on the line are given, we can use the point-slope formula:





Since the slope and a point on the line are given, we can use the point-slope formula:
Compare your answer with the correct one above
What is the equation of a line with slope
and a point
?
What is the equation of a line with slope and a point
?
Since the slope and a point on the line are given, we can use the point-slope formula:

slope:
and point: 






Since the slope and a point on the line are given, we can use the point-slope formula:
slope: and point:
Compare your answer with the correct one above
Consider segment
which passes through the points
and
.
Find the equation of
in the form
.
Consider segment which passes through the points
and
.
Find the equation of in the form
.
Given that JK passes through (4,5) and (144,75) we can find the slope as follows:
Slope is found via:

Plug in and calculate:

Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).


So our answer is:

Given that JK passes through (4,5) and (144,75) we can find the slope as follows:
Slope is found via:
Plug in and calculate:
Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).
So our answer is:
Compare your answer with the correct one above
Determine the equation of a line that has the points
and
?
Determine the equation of a line that has the points and
?
The equation for a line in standard form is written as follows:

Where
is the slope and
is the y intercept. We start by calculating the slope between the two given points using the following formula:

Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:



We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:

The equation for a line in standard form is written as follows:
Where is the slope and
is the y intercept. We start by calculating the slope between the two given points using the following formula:
Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:
We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:
Compare your answer with the correct one above