All SSAT Upper Level Math Resources
Example Questions
Example Question #51 : Geometry
Given the graph of the line below, find the equation of the line.
To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.
Example Question #1 : Lines
Which line passes through the points (0, 6) and (4, 0)?
y = –3/2 – 3
y = 1/5x + 3
y = –3/2x + 6
y = 2/3x –6
y = 2/3 + 5
y = –3/2x + 6
P1 (0, 6) and P2 (4, 0)
First, calculate the slope: m = rise ÷ run = (y2 – y1)/(x2 – x1), so m = –3/2
Second, plug the slope and one point into the slope-intercept formula:
y = mx + b, so 0 = –3/2(4) + b and b = 6
Thus, y = –3/2x + 6
Example Question #101 : Lines
What line goes through the points (1, 3) and (3, 6)?
2x – 3y = 5
4x – 5y = 4
–3x + 2y = 3
3x + 5y = 2
–2x + 2y = 3
–3x + 2y = 3
If P1(1, 3) and P2(3, 6), then calculate the slope by m = rise/run = (y2 – y1)/(x2 – x1) = 3/2
Use the slope and one point to calculate the intercept using y = mx + b
Then convert the slope-intercept form into standard form.
Example Question #101 : Algebra
What is the slope-intercept form of ?
The slope intercept form states that . In order to convert the equation to the slope intercept form, isolate
on the left side:
Example Question #1 : How To Find The Equation Of A Line
A line is defined by the following equation:
What is the slope of that line?
The equation of a line is
y=mx + b where m is the slope
Rearrange the equation to match this:
7x + 28y = 84
28y = -7x + 84
y = -(7/28)x + 84/28
y = -(1/4)x + 3
m = -1/4
Example Question #1 : Lines
If the coordinates (3, 14) and (–5, 15) are on the same line, what is the equation of the line?
First solve for the slope of the line, m using y=mx+b
m = (y2 – y1) / (x2 – x1)
= (15 – 14) / (–5 –3)
= (1 )/( –8)
=–1/8
y = –(1/8)x + b
Now, choose one of the coordinates and solve for b:
14 = –(1/8)3 + b
14 = –3/8 + b
b = 14 + (3/8)
b = 14.375
y = –(1/8)x + 14.375
Example Question #1 : Coordinate Geometry
What is the equation of a line that passes through coordinates and
?
Our first step will be to determing the slope of the line that connects the given points.
Our slope will be . Using slope-intercept form, our equation will be
. Use one of the give points in this equation to solve for the y-intercept. We will use
.
Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.
This is our final answer.
Example Question #251 : Geometry
Which of the following equations does NOT represent a line?
The answer is .
A line can only be represented in the form or
, for appropriate constants
,
, and
. A graph must have an equation that can be put into one of these forms to be a line.
represents a parabola, not a line. Lines will never contain an
term.
Example Question #61 : Coordinate Geometry
Let y = 3x – 6.
At what point does the line above intersect the following:
They do not intersect
(–3,–3)
(0,–1)
(–5,6)
They intersect at all points
They intersect at all points
If we rearrange the second equation it is the same as the first equation. They are the same line.
Example Question #1 : Coordinate Geometry
A line has a slope of and passes through the point
. Find the equation of the line.
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.
Plug the given conditions into the equation to find the -intercept.
Multiply:
Subtract from each side of the equation:
Now that you have solved for , you can write out the full equation of the line:
All SSAT Upper Level Math Resources
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