Intercepts and Curves - Math
Card 0 of 632
True or false: The lines of the equations
and
have the same 
-intercept.
True or false: The lines of the equations
and
have the same
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The 
-intercept of a line is the point at which it intersects the 
-axis; its 
-coordinate at this point is 0, so its 
-coordinate can be found by substituting 0 for 
in the equation and solving for 
. Do this with both equations:
The 
-intercept of the line is at 
.
The 
-intercept of the line is at 
.
The two lines have different 
-intercepts.
The
The
The
The two lines have different
True or false: the lines of the equations
and
have the same 
-intercept.
True or false: the lines of the equations
and
have the same
Tap to see back →
The -intercept of a line is the point at which it intersects the -axis; its -coordinate at this point is 0.
The -coordinate of the line of the equation
can be found by substituting 0 for in the equation and solving for :
The 
-intercept of this line is at 
.
The line with equation 
is a horizontal line with its 
-intercept at 
, so the 
-intercept line of the equation 
has its 
-intercept at 
as well.
Both lines indeed have the same 
-intercept.
The
The
can be found by substituting 0 for
The
The line with equation
Both lines indeed have the same
What is the x-intercept for the line 
?
What is the x-intercept for the line
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To find the x-intercept, plug in 
for 
, since the x-axis is where 
.
add 
to both sides
divide both sides by 
To find the x-intercept, plug in
If a line's 
-intercept is 
. and the 
-intercept is 
, what is the equation of the line?
If a line's
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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
Given the
Add
Divide each side of the equation by
Substituting the value of
By subtracting
Find the 
-intercept of:
Find the
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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
So we first set
turns into
Lets subtract
After doing the arithmetic, we have
Divide by
What is the 
-intercept of:
What is the
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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
Find the y-intercept of the line 
.
Find the y-intercept of the line
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Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is 
.
Plug in 
for 
into the equation to find the y-intercept.
The y-intercept for this line is 
.
Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is
Plug in
The y-intercept for this line is
What is the 
-intercept of:
What is the
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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
After doing the arithmetic we have
Divide both sides by
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
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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
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?
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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
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)
b)
If we hadn't been given multiple options, we could have set up the following equation to figure out the third factor:
Which equation would have an x-intercept at 
and a y-intercept at 
?
Which equation would have an x-intercept at
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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
To determine the slope, divide the change in y by the change in x:
The equation for this line would be
Write the equation of a line with intercepts 
and 
Write the equation of a line with intercepts
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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
The y-intercept in this case is
To find the equation, plug in
This means the equation is
Which equation has the x- and y-intercepts 
and 
?
Which equation has the x- and y-intercepts
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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 can plug in the other intercept's coordinates for
The line is
What are the 
and 
-intercepts of the line defined by the equation:
What are the
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To find the intercepts of a line, we must set the 
and 
values equal to zero and then solve.
To find the intercepts of a line, we must set the
Given the line 
what is the sum of the 
and 
intercepts?
Given the line
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The intercepts cross an axis.
For the 
intercept, set 
to get 
For the 
intercept, set 
to get 
So the sum of the intercepts is 
.
The intercepts cross an axis.
For the
For the
So the sum of the intercepts is
Find the y-intercept of the line 
.
Find the y-intercept of the line
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Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is 
.
Plug in 
for 
into the equation to find the y-intercept.
The y-intercept for this line is 
.
Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is
Plug in
The y-intercept for this line is
What is the 
-intercept of the following line:
What is the
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The 
-intercept is the point where the y-value is equal to 0. Therefore,
The
Which of the following statements regarding the x and y intercepts of the equation 
is true?
Which of the following statements regarding the x and y intercepts of the equation
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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.
To find the x-intercept, we simply plug
Find the 
-intercept of the following function.
Find the
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To find the x-intercept, set y equal to 0.
Now solve for x by dividing by 3 on both sides.
This reduces to,
To find the x-intercept, set y equal to 0.
Now solve for x by dividing by 3 on both sides.
This reduces to,
Find the 
-intercept of the following function.
Find the
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To find the y-intercept, set x equal to 0.
Now solve for y.
To find the y-intercept, set x equal to 0.
Now solve for y.