All SSAT Upper Level Math Resources
Example Questions
Example Question #62 : Geometry
Find the equation of a line that has a slope of and passes through the points
.
In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:
, where
is the slope of the line and
is its
-intercept.
Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the
-intercept. Plug in known values for
and
taken from the given point into the
equation to find the
-intercept:
Multiply:
Subtract from each side of the equation:
Now that you've solved for , you can plug the given slope
and the
-intercept
into the slope-intercept form of the equation of a line to figure out the answer:
Example Question #63 : Geometry
Find the equation of the line that has a slope of and passes through the point
.
In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:
, where
is the slope of the line and
is its
-intercept.
Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the
-intercept. Plug in known values for
and
taken from the given point into the
equation and solve for
to find the
-intercept:
Multiply:
Subtract from each side of the equation:
Now, we can write the final equation by plugging in the given slope and the
-intercept
:
Example Question #64 : Geometry
Find the equation of the line that has a slope of and passes through the point
.
In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:
, where
is the slope of the line and
is its
-intercept.
Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the
-intercept. Plug in known values for
and
taken from the given point into the
equation and solve for
to find the
-intercept:
Multiply:
Add to each side of the equation:
Now, we can write the final equation by plugging in the given slope and the
-intercept
:
Example Question #65 : Geometry
Find the equation of a line that has a slope of and passes through the points
.
In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:
, where
is the slope of the line and
is its
-intercept.
Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the
-intercept. Plug in known values for
and
taken from the given point into the
equation and solve for
to find the
-intercept:
Multiply:
Subtract from both sides of the equation:
Now, we can write the final equation by plugging in the given slope and the
-intercept
:
Example Question #11 : Coordinate Geometry
Find the equation of the line that has a slope of and passes through the point
.
The question gives us both the slope and the -intercept of the line, allowing us to write the following equation by inserting those values into the slope-intercept form of the equation of a line,
:
Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line. Since the problem gives us the slope of the line
, we would just need to use the point that is given to us to find the
-intercept. We could plug in the known values for
and
taken from the given point into the
equation and solve for
to find the
-intercept:
Multiplying leaves us with:
We could then substitute in the given slope and the -intercept into the
equation to arrive at the correct answer:
Example Question #67 : Geometry
Find the equation of a line that has a slope of and passes through the point
.
The question gives us both the slope and the -intercept of the line. Remember that
represents the slope, and
represents the
-intercept to write the following equation:
Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line:
, where
is the slope of the line and
is its
-intercept.
Since the problem gives us the slope of the line , we would just need to use the point that is given to us to find the
-intercept. We could plug in the known values for
and
taken from the given point into the
equation and solve for
to find the
-intercept:
Multiplying leaves us with:
.
We could then substitute in the given slope and the -intercept into the
equation to arrive at the correct answer:
Example Question #71 : Geometry
Find the equation of the line that passes through and
.
First, notice that our -intercept for this line is
; we can tell this because one of the points,
, is on the
-axis since it has a value of
for
.
Now, we need to find the slope of the line. We can do that by using the slope equation:
We can substitute in the values of the provided points—,
,
and
—and then solve for the slope of the line that connects them:
Now, put the two pieces of information together and substitute them into the equation to solve the problem:
Example Question #72 : Geometry
Find the equation of the line that passes through the points and
.
First, notice that our -intercept for this line is
; we can tell this because one of the points,
, is on the
-axis since it has a value of
for
.
Now, we need to find the slope of the line. We can do that by using the slope equation:
We can substitute in the values of the provided points—,
,
and
—and then solve for the slope of the line that connects them:
Now, put the two pieces of information together and substitute them into the equation to solve the problem:
Example Question #73 : Geometry
Find the equation of the line that passes through the points .
First, notice that our -intercept for this line is
; we can tell this because one of the points,
, is on the
-axis since it has a value of
for
.
Now, we need to find the slope of the line. We can do that by using the slope equation:
We can substitute in the values of the provided points—,
,
and
—and then solve for the slope of the line that connects them:
Now, put the two pieces of information together and substitute them into the equation to solve the problem:
Example Question #74 : Geometry
Find the equation of the line that passes through the points and
.
First, we need to find the slope of the line. We can do that by using the slope equation:
We can substitute in the values of the provided points—,
,
and
—and then solve for the slope of the line that connects them:
Next, plug one of the points' coordinates and the slope to the equation and solve for
to find the
-intercept. For this example, let's use the point
:
Multiply:
Change from a whole number to a mixed number with
in the denominator, just like in the fraction
:
Subtract from each side of the equation:
Finally, put the slope and the -intercept into the
equation to arrive at the correct answer:
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All SSAT Upper Level Math Resources
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