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SSAT Upper Level Math : Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #141 : Lines

What is the equation of a line that passes through coordinates $\dpi{100} \small (2,6)$ and $\dpi{100} \small (3,5)$ ?

Possible Answers:

$\dpi{100} \small y=x+7$

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=2x-4$

$\dpi{100} \small y=3x+2$

$\dpi{100} \small y=-x+8$

Correct answer:

$\dpi{100} \small y=-x+8$

Explanation:

Our first step will be to determing the slope of the line that connects the given points.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{2-3}=\frac{1}{-1}=-1$

Our slope will be . Using slope-intercept form, our equation will be y=(-1)x+b . Use one of the give points in this equation to solve for the y-intercept. We will use $\dpi{100} \small (2,6)$ .

6=(-1)(2)+b

6=-2+b

8=b

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

y=(-1)x+8

y=-x+8

This is our final answer.

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Example Question #2 : Other Lines

Which of the following equations does NOT represent a line?

Possible Answers:

x=10

x-y=10

5y=10

x+y=10

x^2+y=10

Correct answer:

x^2+y=10

Explanation:

The answer is x^2+y=10 .

A line can only be represented in the form x=z or y=mx+b , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

x^2+y=10 represents a parabola, not a line. Lines will never contain an x^2 term.

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Example Question #41 : Other Lines

Let y = 3x – 6.

At what point does the line above intersect the following:

$2x =\frac{2}{3}y+4$

Possible Answers:

(–5,6)

(–3,–3)

They do not intersect

(0,–1)

They intersect at all points

Correct answer:

They intersect at all points

Explanation:

If we rearrange the second equation it is the same as the first equation. They are the same line.

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Example Question #2 : Lines

A line has a slope of and passes through the point (8, 1) . Find the equation of the line.

Possible Answers:

y=15x+2

y=2x+1

y=2x-15

y=2x-10

Correct answer:

y=2x-15

Explanation:

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:

y=mx+b , where is the slope of the line and is its -intercept.

Plug the given conditions into the equation to find the -intercept.

1=2(8)+b

Multiply:

b+16=1

Subtract from each side of the equation:

b=-15

Now that you have solved for , you can write out the full equation of the line:

y=2x-15

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Example Question #62 : Geometry

Find the equation of a line that has a slope of and passes through the points (-2, 2) .

Possible Answers:

y=2x-2

y=2x+2

y=-2x+2

y=-2x-2

Correct answer:

y=-2x-2

Explanation:

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:

y=mx+b , where is the slope of the line and is its -intercept.

Since the problem gives us the slope of the line (m) , 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 y=mx+b equation to find the -intercept:

2=-2(-2)+b

Multiply:

b+4=2

Subtract from each side of the equation:

b=-2

Now that you've solved for , you can plug the given slope (m) and the -intercept (b) into the slope-intercept form of the equation of a line to figure out the answer:

y=-2x-2

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Example Question #63 : Geometry

Find the equation of the line that has a slope of and passes through the point (-5, 4) .

Possible Answers:

y=-3x-3

y=-3x-9

y=-3x+11

y=-3x-11

Correct answer:

y=-3x-11

Explanation:

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:

y=mx+b , where is the slope of the line and is its -intercept.

4=-3(-5)+b

Multiply:

4=15+b

Subtract from each side of the equation:

b=-11

Now, we can write the final equation by plugging in the given slope (m) and the -intercept (b) :

y=-3x-11

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Example Question #64 : Geometry

Find the equation of the line that has a slope of and passes through the point (-1, -1) .

Possible Answers:

y=4x-9

y=4x+3

y=4x-3

y=4x+8

Correct answer:

y=4x+3

Explanation:

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:

y=mx+b , where is the slope of the line and is its -intercept.

-1=4(-1)+b

Multiply:

-1=-4+b

Add to each side of the equation:

b=3

Now, we can write the final equation by plugging in the given slope (m) and the -intercept (b) :

y=4x+3

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Example Question #65 : Geometry

Find the equation of a line that has a slope of $\frac{1}{2}$ and passes through the points (4, -1) .

Possible Answers:

$y=\frac{1}{2}x-3$

$y=-\frac{1}{2}x-3$

$y=-\frac{1}{2}x+3$

$y=\frac{1}{2}x+3$

Correct answer:

$y=\frac{1}{2}x-3$

Explanation:

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:

y=mx+b , where is the slope of the line and is its -intercept.

$-1=\frac{1}{2}(4)+b$

Multiply:

-1=2+b

Subtract from both sides of the equation:

b=-3

Now, we can write the final equation by plugging in the given slope (m) and the -intercept (b) :

$y=\frac{1}{2}x-3$

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Example Question #11 : Coordinate Geometry

Find the equation of the line that has a slope of and passes through the point (0, 5) .

Possible Answers:

y=2x-9

y=2x-5

y=-2x+5

y=2x+5

Correct answer:

y=2x+5

Explanation:

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, y=mx+b :

y=2x+5

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 (m) , 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 y=mx+b equation and solve for to find the -intercept:

5=2(0)+b

Multiplying leaves us with:

b=5

We could then substitute in the given slope and the -intercept into the y=mx+b equation to arrive at the correct answer:

y=2x+5

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Example Question #67 : Geometry

Find the equation of a line that has a slope of and passes through the point (0, -2) .

Possible Answers:

y=-x

y=-x-2

y=x+2

y=-x-1

Correct answer:

y=-x-2

Explanation:

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:

y=-x-2

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:

y=mx+b , where is the slope of the line and is its -intercept.

Since the problem gives us the slope of the line (m) , 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 y=mx+b equation and solve for to find the -intercept:

-2=-1(0)+b

Multiplying leaves us with:

b=-2 .

We could then substitute in the given slope and the -intercept into the y=mx+b equation to arrive at the correct answer:

y=-x-2

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SSAT Upper Level Math : Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #141 : Lines

Example Question #2 : Other Lines

Example Question #41 : Other Lines

Example Question #2 : Lines

Example Question #62 : Geometry

Example Question #63 : Geometry

Example Question #64 : Geometry

Example Question #65 : Geometry

Example Question #11 : Coordinate Geometry

Example Question #67 : Geometry

All SSAT Upper Level Math Resources

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