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SSAT Upper Level Math : Coordinate Geometry

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Example Questions

Example Question #201 : Coordinate Geometry

Function 1

What equation is graphed in the above figure?

Possible Answers:

$y = \left \lceil x\right \rceil+ 4$

$y = \left \lfloor x\right \rfloor - 4$

$y = \left \lceil x\right \rceil+ 5$

$y = \left \lfloor x\right \rfloor + 5$

$y = \left \lfloor x\right \rfloor + 4$

Correct answer:

$y = \left \lceil x\right \rceil+ 4$

Explanation:

The least integer function, or celing function, $f(x) = \left \lceil x\right \rceil$ , pairs each value of with the least integer greater than or equal to . Its graph is below.

Ceiling function

The given graph is the above graph shifted upward four units. The graph of any function y = f(x) shifted upward four units is y = f(x) + 4 , so the given graph corresponds to equation $y = \left \lceil x\right \rceil+ 4$ .

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Example Question #12 : Transformation

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |x-5|

y = |x| + 5

y = |x| -5

y = |5x|

y = |x+5|

Correct answer:

y = |x| + 5

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the above graph shifted upward five units. The graph of any function y = f(x) shifted upward five units is y = f(x)+5 , so the correct response is y = |x| + 5 .

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Example Question #251 : Geometry

What is the slope of the line that passes through the points $(-1,4) \text{ and } (-5,1)$ ?

Possible Answers:

$-\frac{3}{4}$

$\frac{4}{3}$

$-\frac{4}{3}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values from the points given, we get the following slope:

$\text{Slope}=\frac{1-4}{-5-(-1)}=\frac{-3}{-4}=\frac{3}{4}$

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Example Question #252 : Geometry

Find the slope of a line that passes through the points (17,2) and (-2, -1) .

Possible Answers:

$-\frac{19}{3}$

$\frac{3}{19}$

$\frac{19}{3}$

$-\frac{3}{19}$

Correct answer:

$\frac{3}{19}$

Explanation:

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-1-2}{-2-17}=\frac{-3}{-19}=\frac{3}{19}$

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Example Question #253 : Geometry

Find the slope of the line that passes through the points (a, b) and (2, 3) .

Possible Answers:

$\frac{3-b}{2-a}$

$\frac{2-a}{3-b}$

$\frac{2-b}{3-a}$

$\frac{3-a}{2-b}$

Correct answer:

$\frac{3-b}{2-a}$

Explanation:

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{3-b}{2-a}$

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Example Question #1 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

A line has the equation 5x-9y=12 . What is the slope of this line?

Possible Answers:

$\frac{5}{9}$

$-\frac{4}{3}$

$\frac{9}{5}$

Correct answer:

$\frac{5}{9}$

Explanation:

You need to put the equation in y=mx+b form before you can easily find out its slope.

5x-9y=12

-9y=-5x+12

$y=\frac{5}{9}x-\frac{4}{3}$

Since $m=\frac{5}{9}$ , that must be the slope.

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Example Question #201 : Coordinate Geometry

Find the slope of the line that goes through the points (4t, 8s) and (2t, -9s) .

Possible Answers:

$\frac{6t}{-s}$

$\frac{17s}{2t}$

$\frac{-s}{6t}$

$\frac{2t}{17s}$

Correct answer:

$\frac{17s}{2t}$

Explanation:

Even though there are variables involved in the coordinates of these points, you can still use the slope formula to figure out the slope of the line that connects them.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-9s-8s}{2t-4t}=\frac{-17s}{-2t}=\frac{17s}{2t}$

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Example Question #2 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

The equation of a line is 12x-8y=6 . Find the slope of this line.

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

$\frac{3}{4}$

$-\frac{3}{4}$

Correct answer:

$\frac{3}{2}$

Explanation:

To find the slope, you will need to put the equation in y=mx+b form. The value of will be the slope.

12x-8y=6

Subtract from either side:

8y=12x-6

Divide each side by :

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

You can now easily identify the value of .

$m=\frac{3}{2}$

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Example Question #202 : Coordinate Geometry

Find the slope of the line that passes through the points (0,3) and (8,1) .

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{4}$

Correct answer:

$-\frac{1}{4}$

Explanation:

You can use the slope formula to figure out the slope of the line that connects these two points. Just substitute the specified coordinates into the equation and then subtract:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{3-1}{0-8}=\frac{2}{-8}=-\frac{1}{4}$

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Example Question #263 : Geometry

Find the slope of the following function: 2x-6y=3

Possible Answers:

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

Rewrite the equation in slope-intercept form, y=mx+b .

2x-6y=3

2x=3+6y

2x-3=6y

$\frac{2x-3}{6}=y$

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

The slope is the term, which is $\frac{1}{3}$ .

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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 #201 : Coordinate Geometry

Example Question #12 : Transformation

Example Question #251 : Geometry

Example Question #252 : Geometry

Example Question #253 : Geometry

Example Question #1 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Example Question #201 : Coordinate Geometry

Example Question #2 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Example Question #202 : Coordinate Geometry

Example Question #263 : Geometry

All SSAT Upper Level Math Resources

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