How to find the equation of a curve - Intermediate Geometry
Card 0 of 9
If a line's 
-intercept is 
. and the 
-intercept is 
, what is the equation of the line?
If a line's
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
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Find the 
-intercept of:
Find the
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
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What is the 
-intercept of:
What is the
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
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What is the 
-intercept of:
What is the
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
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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
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
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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
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:
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Which equation would have an x-intercept at 
and a y-intercept at 
?
Which equation would have an x-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
To determine the slope, divide the change in y by the change in x:
The equation for this line would be
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Write the equation of a line with intercepts 
and 
Write the equation of a line with intercepts
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
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Which equation has the x- and y-intercepts 
and 
?
Which equation has the x- and y-intercepts
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
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