Intercepts and Curves - High School Math
Card 0 of 20
The center of a circle is 
and its radius is 
. Which of the following could be the equation of the circle?
The center of a circle is
The general equation of a circle is 
, where the center of the circle is 
and the radius is 
.
Thus, we plug the values given into the above equation to get 
.
The general equation of a circle is
Thus, we plug the values given into the above equation to get
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Which one of these equations accurately describes a circle with a center of 
and a radius of 
?
Which one of these equations accurately describes a circle with a center of
The standard formula for a circle is 
, with 
the center of the circle and 
the radius.
Plug in our given information.
This describes what we are looking for. This equation is not one of the answer choices, however, so subtract 
from both sides.
The standard formula for a circle is
Plug in our given information.
This describes what we are looking for. This equation is not one of the answer choices, however, so subtract
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What line goes through points 
and 
?
What line goes through points
First, we find the slope between the two points:
and 
Plug the slope and one point into the slope-intercept form to calculate the intercept:
Thus the equation between the points becomes 
.
First, we find the slope between the two points:
Plug the slope and one point into the slope-intercept form to calculate the intercept:
Thus the equation between the points becomes
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A straight line passes through the points 
and 
.
What is the 
-intercept of this line?
A straight line passes through the points
What is the
First calculate the slope:
The standard equation for a line is 
.
In this equation, 
is the slope of the line, and 
is the 
-intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).
Plugging in (1,3) we get 
.
Therefore, 
.
Our equation for the line is now:
To find the 
-intercept, we plug in 
:
Thus, the 
-intercept the point (4,0).
First calculate the slope:
The standard equation for a line is
In this equation,
Plugging in (1,3) we get
Therefore,
Our equation for the line is now:
To find the
Thus, the
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What is the x-intercept of the following equation?
What is the x-intercept of the following equation?
We want to find the x-intercept, which is the point at which the graph crosses the x-axis. Every point on the x-axis has a y-value of 0. Thus, to find the x-intercept we just need to plug 0 in for y.
Thus, 
.
Dividing both sides by 
, we get 
.
We want to find the x-intercept, which is the point at which the graph crosses the x-axis. Every point on the x-axis has a y-value of 0. Thus, to find the x-intercept we just need to plug 0 in for y.
Thus,
Dividing both sides by
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Calculate the y-intercept of the line depicted by the equation below.
Calculate the y-intercept of the line depicted by the equation below.
To find the y-intercept, let 
equal 0.
We can then solve for the value of 
.
The y-intercept will be 
.
To find the y-intercept, let
We can then solve for the value of
The y-intercept will be
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What is the y-intercept of the equation?
What is the y-intercept of the equation?
To find the y-intercept, we set the 
value equal to zero and solve for the 
value.
Since the y-intercept is a point, we will need to convert our answer to point notation.
To find the y-intercept, we set the
Since the y-intercept is a point, we will need to convert our answer to point notation.
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What is the x-intercept of the equation?
What is the x-intercept of the equation?
To find the x-intercept of an equation, set the 
value equal to zero and solve for 
.
Subtract 
from both sides.
Multiply both sides by 
.
Since the x-intercept is a point, we will want to write it in point notation: 
To find the x-intercept of an equation, set the
Subtract
Multiply both sides by
Since the x-intercept is a point, we will want to write it in point notation:
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What is the y-intercept of the equation?
What is the y-intercept of the equation?
To find the y-intercept, we set the 
value equal to zero and solve for the value of 
.
Since the y-intercept is a point, we want to write our answer in point notation: 
.
To find the y-intercept, we set the
Since the y-intercept is a point, we want to write our answer in point notation:
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What is the 
-intercept of the equation?
What is the
To find the x-intercept of an equation, set the 
value equal to zero and solve for 
.
Subtract 
from both sides.
Divide both sides by 
.
Since the x-intercept is a point, we will write our answer in point notation: 
.
To find the x-intercept of an equation, set the
Subtract
Divide both sides by
Since the x-intercept is a point, we will write our answer in point notation:
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What is the x-intercept of 
?
What is the x-intercept of
To find the x-intercept, set y equal to zero and solve:
Subtract 
from both sides:
Divide both sides by 
to isolate x:
To find the x-intercept, set y equal to zero and solve:
Subtract
Divide both sides by
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What is the y-intercept of 
?
What is the y-intercept of
To find the y-intercept, set the x value to zero and solve:
To find the y-intercept, set the x value to zero and solve:
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What is the y-intercept of 
What is the y-intercept of
To solve for the y-intercept, set the x value equal to zero:
To solve for the y-intercept, set the x value equal to zero:
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What is the x-intercept of 
?
What is the x-intercept of
To solve for the x-intercept, set the y value equal to zero:
Subtract 
from both sides:
To solve for the x-intercept, set the y value equal to zero:
Subtract
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What is the y-intercept of 
?
What is the y-intercept of
Isolate for 
so that the equation is in slope-intercept form 
.
The 
is the y-intercept, which in this case, is 
.
Isolate for
The
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What are the 
-intercepts of 
?
What are the
Factor out an 
from the original equation so that it is 
.
Set that expressions equal to 
so that you can find the 
-intercepts. Your answers are 
and 
.
Factor out an
Set that expressions equal to
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Find the 
-intercept of 
.
Find the
Put the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
-5y = 3x + 10
y = (-3/5)x + 10/(-5)
Now we can easily see that 
is the 
-intercept.
Put the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
-5y = 3x + 10
y = (-3/5)x + 10/(-5)
Now we can easily see that
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Find the 
-intercepts of 
Find the
Take out a 
from the original equation so that you can set the expression 
equal to 
and get your 
-intercepts 
and 
.
Take out a
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What is the y-intercept of the following curve?
What is the y-intercept of the following curve?
The y-intercept of a curve is the value of that curve when the x-coordinate is 
. Thus, we plug in 
to our equation, yielding 
.
The y-intercept of a curve is the value of that curve when the x-coordinate is
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What is the y-intercept of 
?
What is the y-intercept of
When looking at an equation in standard 
form, 
is our y-intercept.
Or, set the 
value equal to 
and solve.
When looking at an equation in standard
Or, set the
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