How to find the equation of a curve - Geometry
Card 0 of 36
If a line's
-intercept is
. and the
-intercept is
, what is the equation of the line?
If a line's -intercept is
. and the
-intercept is
, what is the equation of the line?
Write the equation in slope-intercept form:

We were given the
-intercept,
, which means
:

Given the
-intercept is
, the point existing on the line is
. Substitute this point into the slope-intercept equation and then solve for
to find the slope:

Add
to each side of the equation:

Divide each side of the equation by
:

Substituting the value of
back into the slope-intercept equation, we get:

By subtracting
on both sides, we can rearrange the equation to put it into standard form:

Write the equation in slope-intercept form:
We were given the -intercept,
, which means
:
Given the -intercept is
, the point existing on the line is
. Substitute this point into the slope-intercept equation and then solve for
to find the slope:
Add to each side of the equation:
Divide each side of the equation by :
Substituting the value of back into the slope-intercept equation, we get:
By subtracting on both sides, we can rearrange the equation to put it into standard form:
Compare your answer with the correct one above
Find the
-intercept of:

Find the -intercept of:
To find the x-intercept, we need to find the value of
when
.
So we first set
to zero.

turns into

Lets subtract
from both sides to move
to one side of the equation.

After doing the arithmetic, we have
.
Divide by
from both sides


To find the x-intercept, we need to find the value of when
.
So we first set to zero.
turns into
Lets subtract from both sides to move
to one side of the equation.
After doing the arithmetic, we have
.
Divide by from both sides
Compare your answer with the correct one above
What is the
-intercept of:

What is the -intercept of:
To find the y-intercept, we set 
So

turns into
.
After doing the arithmetic we get
.
To find the y-intercept, we set
So
turns into
.
After doing the arithmetic we get
.
Compare your answer with the correct one above
What is the
-intercept of:

What is the -intercept of:
The x-intercept can be found where 
So

turns into
.
Lets subtract
from both sides to solve for
.

After doing the arithmetic we have
.
Divide both sides by 


The x-intercept can be found where
So
turns into
.
Lets subtract from both sides to solve for
.
After doing the arithmetic we have
.
Divide both sides by
Compare your answer with the correct one above
Suppose two intercepts create a line. If the
-intercept is
and
-intercept is
, what is the equation of the line?
Suppose two intercepts create a line. If the -intercept is
and
-intercept is
, what is the equation of the line?
Rewrite the intercepts in terms of points.
X-intercept of 1:
.
Y-intercept of 2: 
Write the slope-intercept form for linear equations.

Substititute the y-intercept into the slope-intercept equation.


Substitute both the x-intercept point and the y-intercept into the equation to solve for slope.


Rewrite by substituting the values of
and
into the y-intercept form.

Rewrite the intercepts in terms of points.
X-intercept of 1: .
Y-intercept of 2:
Write the slope-intercept form for linear equations.
Substititute the y-intercept into the slope-intercept equation.
Substitute both the x-intercept point and the y-intercept into the equation to solve for slope.
Rewrite by substituting the values of and
into the y-intercept form.
Compare your answer with the correct one above
Which equation has a y-intercept at 2 and x-intercepts at -1 and 6?
Which equation has a y-intercept at 2 and x-intercepts at -1 and 6?
In order for the equation to have x-intercepts at -1 and 6, it must have
and
as factors. This leaves us with only 2 choices,
or 
This equation must also have a y-intercept of 2. This means that plugging in 0 for x will gives us a y-value of 2. Because we have two options, we could plug in 0 for x in each to see which gives us an answer of 2:
a)
we can eliminate that choice
b)
this must be the right choice.
If we hadn't been given multiple options, we could have set up the following equation to figure out the third factor:


divide by -6

In order for the equation to have x-intercepts at -1 and 6, it must have and
as factors. This leaves us with only 2 choices,
or
This equation must also have a y-intercept of 2. This means that plugging in 0 for x will gives us a y-value of 2. Because we have two options, we could plug in 0 for x in each to see which gives us an answer of 2:
a) we can eliminate that choice
b) this must be the right choice.
If we hadn't been given multiple options, we could have set up the following equation to figure out the third factor:
divide by -6
Compare your answer with the correct one above
Which equation would have an x-intercept at
and a y-intercept at
?
Which equation would have an x-intercept at and a y-intercept at
?
We're writing the equation for a line passing through the points
and
. Since we already know the y-intercept, we can figure out the slope of this line and then write a slope-intercept equation.
To determine the slope, divide the change in y by the change in x:

The equation for this line would be
.
We're writing the equation for a line passing through the points and
. Since we already know the y-intercept, we can figure out the slope of this line and then write a slope-intercept equation.
To determine the slope, divide the change in y by the change in x:
The equation for this line would be .
Compare your answer with the correct one above
Write the equation of a line with intercepts
and 
Write the equation of a line with intercepts and
The line will eventually be in the form
where
is the y-intercept.
The y-intercept in this case is
.
To find the equation, plug in
for
, and the other point,
as x and y:

add
to both sides

This means the equation is 
The line will eventually be in the form where
is the y-intercept.
The y-intercept in this case is .
To find the equation, plug in for
, and the other point,
as x and y:
add
to both sides
This means the equation is
Compare your answer with the correct one above
Which equation has the x- and y-intercepts
and
?
Which equation has the x- and y-intercepts and
?
Since this line has the y-intercept
, we know that in the form
, 
We can plug in the other intercept's coordinates for
and
to solve for
:

subtract 
divide by 

The line is 
Since this line has the y-intercept , we know that in the form
,
We can plug in the other intercept's coordinates for and
to solve for
:
subtract
divide by
The line is
Compare your answer with the correct one above
If a line's
-intercept is
. and the
-intercept is
, what is the equation of the line?
If a line's -intercept is
. and the
-intercept is
, what is the equation of the line?
Write the equation in slope-intercept form:

We were given the
-intercept,
, which means
:

Given the
-intercept is
, the point existing on the line is
. Substitute this point into the slope-intercept equation and then solve for
to find the slope:

Add
to each side of the equation:

Divide each side of the equation by
:

Substituting the value of
back into the slope-intercept equation, we get:

By subtracting
on both sides, we can rearrange the equation to put it into standard form:

Write the equation in slope-intercept form:
We were given the -intercept,
, which means
:
Given the -intercept is
, the point existing on the line is
. Substitute this point into the slope-intercept equation and then solve for
to find the slope:
Add to each side of the equation:
Divide each side of the equation by :
Substituting the value of back into the slope-intercept equation, we get:
By subtracting on both sides, we can rearrange the equation to put it into standard form:
Compare your answer with the correct one above
Find the
-intercept of:

Find the -intercept of:
To find the x-intercept, we need to find the value of
when
.
So we first set
to zero.

turns into

Lets subtract
from both sides to move
to one side of the equation.

After doing the arithmetic, we have
.
Divide by
from both sides


To find the x-intercept, we need to find the value of when
.
So we first set to zero.
turns into
Lets subtract from both sides to move
to one side of the equation.
After doing the arithmetic, we have
.
Divide by from both sides
Compare your answer with the correct one above
What is the
-intercept of:

What is the -intercept of:
To find the y-intercept, we set 
So

turns into
.
After doing the arithmetic we get
.
To find the y-intercept, we set
So
turns into
.
After doing the arithmetic we get
.
Compare your answer with the correct one above
What is the
-intercept of:

What is the -intercept of:
The x-intercept can be found where 
So

turns into
.
Lets subtract
from both sides to solve for
.

After doing the arithmetic we have
.
Divide both sides by 


The x-intercept can be found where
So
turns into
.
Lets subtract from both sides to solve for
.
After doing the arithmetic we have
.
Divide both sides by
Compare your answer with the correct one above
Suppose two intercepts create a line. If the
-intercept is
and
-intercept is
, what is the equation of the line?
Suppose two intercepts create a line. If the -intercept is
and
-intercept is
, what is the equation of the line?
Rewrite the intercepts in terms of points.
X-intercept of 1:
.
Y-intercept of 2: 
Write the slope-intercept form for linear equations.

Substititute the y-intercept into the slope-intercept equation.


Substitute both the x-intercept point and the y-intercept into the equation to solve for slope.


Rewrite by substituting the values of
and
into the y-intercept form.

Rewrite the intercepts in terms of points.
X-intercept of 1: .
Y-intercept of 2:
Write the slope-intercept form for linear equations.
Substititute the y-intercept into the slope-intercept equation.
Substitute both the x-intercept point and the y-intercept into the equation to solve for slope.
Rewrite by substituting the values of and
into the y-intercept form.
Compare your answer with the correct one above
Which equation has a y-intercept at 2 and x-intercepts at -1 and 6?
Which equation has a y-intercept at 2 and x-intercepts at -1 and 6?
In order for the equation to have x-intercepts at -1 and 6, it must have
and
as factors. This leaves us with only 2 choices,
or 
This equation must also have a y-intercept of 2. This means that plugging in 0 for x will gives us a y-value of 2. Because we have two options, we could plug in 0 for x in each to see which gives us an answer of 2:
a)
we can eliminate that choice
b)
this must be the right choice.
If we hadn't been given multiple options, we could have set up the following equation to figure out the third factor:


divide by -6

In order for the equation to have x-intercepts at -1 and 6, it must have and
as factors. This leaves us with only 2 choices,
or
This equation must also have a y-intercept of 2. This means that plugging in 0 for x will gives us a y-value of 2. Because we have two options, we could plug in 0 for x in each to see which gives us an answer of 2:
a) we can eliminate that choice
b) this must be the right choice.
If we hadn't been given multiple options, we could have set up the following equation to figure out the third factor:
divide by -6
Compare your answer with the correct one above
Which equation would have an x-intercept at
and a y-intercept at
?
Which equation would have an x-intercept at and a y-intercept at
?
We're writing the equation for a line passing through the points
and
. Since we already know the y-intercept, we can figure out the slope of this line and then write a slope-intercept equation.
To determine the slope, divide the change in y by the change in x:

The equation for this line would be
.
We're writing the equation for a line passing through the points and
. Since we already know the y-intercept, we can figure out the slope of this line and then write a slope-intercept equation.
To determine the slope, divide the change in y by the change in x:
The equation for this line would be .
Compare your answer with the correct one above
Write the equation of a line with intercepts
and 
Write the equation of a line with intercepts and
The line will eventually be in the form
where
is the y-intercept.
The y-intercept in this case is
.
To find the equation, plug in
for
, and the other point,
as x and y:

add
to both sides

This means the equation is 
The line will eventually be in the form where
is the y-intercept.
The y-intercept in this case is .
To find the equation, plug in for
, and the other point,
as x and y:
add
to both sides
This means the equation is
Compare your answer with the correct one above
Which equation has the x- and y-intercepts
and
?
Which equation has the x- and y-intercepts and
?
Since this line has the y-intercept
, we know that in the form
, 
We can plug in the other intercept's coordinates for
and
to solve for
:

subtract 
divide by 

The line is 
Since this line has the y-intercept , we know that in the form
,
We can plug in the other intercept's coordinates for and
to solve for
:
subtract
divide by
The line is
Compare your answer with the correct one above
If a line's
-intercept is
. and the
-intercept is
, what is the equation of the line?
If a line's -intercept is
. and the
-intercept is
, what is the equation of the line?
Write the equation in slope-intercept form:

We were given the
-intercept,
, which means
:

Given the
-intercept is
, the point existing on the line is
. Substitute this point into the slope-intercept equation and then solve for
to find the slope:

Add
to each side of the equation:

Divide each side of the equation by
:

Substituting the value of
back into the slope-intercept equation, we get:

By subtracting
on both sides, we can rearrange the equation to put it into standard form:

Write the equation in slope-intercept form:
We were given the -intercept,
, which means
:
Given the -intercept is
, the point existing on the line is
. Substitute this point into the slope-intercept equation and then solve for
to find the slope:
Add to each side of the equation:
Divide each side of the equation by :
Substituting the value of back into the slope-intercept equation, we get:
By subtracting on both sides, we can rearrange the equation to put it into standard form:
Compare your answer with the correct one above
Find the
-intercept of:

Find the -intercept of:
To find the x-intercept, we need to find the value of
when
.
So we first set
to zero.

turns into

Lets subtract
from both sides to move
to one side of the equation.

After doing the arithmetic, we have
.
Divide by
from both sides


To find the x-intercept, we need to find the value of when
.
So we first set to zero.
turns into
Lets subtract from both sides to move
to one side of the equation.
After doing the arithmetic, we have
.
Divide by from both sides
Compare your answer with the correct one above