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SSAT Upper Level Math : Coordinate Geometry

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Example Questions

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Example Question #10 :How To Find The Equation Of A Line

Given the graph of the line below, find the equation of the line.

Act_math_160_04

Possible Answers:

y=-x

y=x-4

y=-5x-4

$y=\frac{10}{3}x-4$

Correct answer:

$y=\frac{10}{3}x-4$

Explanation:

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.

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Example Question #2 :How To Find The Equation Of A Line

Which line passes through the points (0, 6) and (4, 0)?

Possible Answers:

y = –3/2x + 6

y = –3/2 – 3

y = 2/3 + 5

y = 2/3x –6

y = 1/5x + 3

Correct answer:

y = –3/2x + 6

Explanation:

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

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Example Question #1 :How To Find The Equation Of A Line

What line goes through the points (1, 3) and (3, 6)?

Possible Answers:

3x + 5y = 2

2x – 3y = 5

–2x + 2y = 3

–3x + 2y = 3

4x – 5y = 4

Correct answer:

–3x + 2y = 3

Explanation:

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.

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Example Question #2 :How To Find The Equation Of A Line

What is the slope-intercept form of $\dpi{100} \small 8x-2y-12=0$ ?

Possible Answers:

$\dpi{100} \small y=-4x+6$

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

$\dpi{100} \small y=4x+6$

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

$\dpi{100} \small y=4x-6$

Correct answer:

$\dpi{100} \small y=4x-6$

Explanation:

The slope intercept form states that $\dpi{100} \small y=mx+b$ . In order to convert the equation to the slope intercept form, isolate $\dpi{100} \small y$ on the left side:

$\dpi{100} \small 8x-2y=12$

$\dpi{100} \small -2y=-8x+12$

$\dpi{100} \small y=4x-6$

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Example Question #3 :How To Find The Equation Of A Line

A line is defined by the following equation:

7x+28y=84

What is the slope of that line?

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$-\frac{1}{4}$

Explanation:

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7 x + y = 28日84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

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Example Question #141 :Coordinate Geometry

If the coordinates (3, 14) and (–5, 15) are on the same line, what is the equation of the line?

Possible Answers:

$y=-\frac{1}{8}x+14.375$

y=-8x-38

$y=\frac{1}{8}x+14.375$

$y=-\frac{1}{8}x+13.625$

y=-8x+38

Correct answer:

$y=-\frac{1}{8}x+14.375$

Explanation:

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

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Example Question #142 :Coordinate Geometry

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

Possible Answers:

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

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

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

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

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

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 #143 :Coordinate Geometry

Which of the following equations does NOT represent a line?

Possible Answers:

x^2+y=10

5y=10

x+y=10

x-y=10

x=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 #2 :Lines

Let y = 3x– 6.

At what point does the line above intersect the following:

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

Possible Answers:

(0,–1)

They do not intersect

(–3,–3)

They intersect at all points

(–5,6)

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 :Coordinate Geometry

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

Possible Answers:

y=2x+1

y=2x-15

y=15x+2

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 , whereis the slope of the line andis its-intercept.

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

1=2(8)+b

Multiply:

b+16=1

Subtractfrom 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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SSAT Upper Level Math : Coordinate Geometry

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #10 :How To Find The Equation Of A Line

Example Question #2 :How To Find The Equation Of A Line

Example Question #1 :How To Find The Equation Of A Line

Example Question #2 :How To Find The Equation Of A Line

Example Question #3 :How To Find The Equation Of A Line

Example Question #141 :Coordinate Geometry

Example Question #142 :Coordinate Geometry

Example Question #143 :Coordinate Geometry

Example Question #2 :Lines

Example Question #2 :Coordinate Geometry

All SSAT Upper Level Math Resources

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