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SSAT Upper Level Math : Geometry

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Example Questions

Example Question #483 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

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

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

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

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

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 #91 : Expressions & Equations

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 #1 : How To Find Slope

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 #1 : Slope

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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Example Question #3 : How To Find Slope

Find the slope of the line given the two points: $(5,8) \textup{ and } (-3,-7)$

Possible Answers:

$\frac{8}{15}$

$\frac{4}{3}$

$-\frac{15}{8}$

$\frac{15}{8}$

$-\frac{8}{15}$

Correct answer:

$\frac{15}{8}$

Explanation:

Write the formula to find the slope.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{y_1-y_2}{x_1-x_2}$

Either equation will work. Let's choose the latter. Substitute the points.

$m=\frac{y_1-y_2}{x_1-x_2}=\frac{8-(-7)}{5-(-3)}= \frac{15}{8}$

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Example Question #2 : Slope

What is the slope of the line with the equation 2x+3y=-9?

Possible Answers:

$-\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$-\frac{2}{3}$

Explanation:

To find the slope, put the equation in the form of y=mx+b .

2x+3y=-9

3y=-2x-9

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

Since $m=-\frac{2}{3}$ , that is the value of the slope.

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Example Question #11 : How To Find Slope

Consider the line of the equation f(x) = 5x - 17 . The line of a function g(x) has the same slope as that of f(x) . Which of the following could be the definition of g(x) ?

Possible Answers:

g (x) = 5x - 34

g(x) =10x - 34

g(x) = 10 x - 17

g(x) = 17x - 5

Correct answer:

g (x) = 5x - 34

Explanation:

The definition of f(x) is written in slope-intercept form f(x )= mx + b , in which , the coefficient of , is the slope of its line. f(x) = 5x - 17 , so the slope of its line is m = 5 .

We must select the choice whose line has this slope. The definition of g(x) in each choice is also written in slope-intercept form, so we select the alternative with -coefficient 5; the only such alternative is g (x) = 5x - 34 .

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Example Question #1 : How To Find X Or Y Intercept

What is the -intercept of the graph of the function $f \left ( x\right ) = 2x^{2} - 7x + 5$ ?

Possible Answers:

$\left (0,5 \right )$

$\left (0,-7 \right )$

$\left ( 0, -3 \frac{1}{2}\right )$

$\left (0,2 \right )$

$\left (0,0 \right )$

Correct answer:

$\left (0,5 \right )$

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis - that is, at which x = 0 . This point is $\left (0, f(0) \right )$ , so evaluate f(0) :

$f \left ( x\right ) = 2x^{2} - 7x + 5$

$f \left (0\right ) = 2 \cdot 0^{2} - 7 \cdot 0 + 5$

$f \left (0\right ) = 0- 0 + 5 = 5$

The -intercept is $\left (0,5 \right )$ .

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Example Question #1 : How To Find X Or Y Intercept

Give the -intercept, if there is one, of the graph of the equation

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

Possible Answers:

(0,3)

$\left ( 0, \frac{3}{2}\right )$

(0,4)

The graph has no -intercept.

(0,2)

Correct answer:

The graph has no -intercept.

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

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

$y = \frac{1}{0^{2}+0} + 3$

$y = \frac{1}{0} + 3$

However, since this expression has 0 in a denominator, it is of undefined value. This means that there is no value of paired with -coordinate 0, and, subsequently, the graph of the equation has no -intercept.

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Example Question #2 : How To Find X Or Y Intercept

Give the -intercept, if there is one, of the graph of the equation

$y = \frac{3}{\left | 3x-8\right |}$

Possible Answers:

$\left ( 0,- \frac{3}{5}\right )$

$\left ( 0, -\frac{3}{8}\right )$

$\left ( 0, \frac{3}{5}\right )$

The graph has no -intercept.

$\left ( 0, \frac{3}{8}\right )$

Correct answer:

$\left ( 0, \frac{3}{8}\right )$

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

$y = \frac{3}{\left | 3x-8\right |}$

$y = \frac{3}{\left | 3 \cdot 0 -8\right |}$

$y = \frac{3}{\left | 0 -8\right |}$

$y = \frac{3}{\left | -8\right |}$

$y = \frac{3}{ 8}$

The -intercept is $\left ( 0, \frac{3}{8}\right )$ .

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All SSAT Upper Level Math Resources

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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 #483 : Ssat Upper Level Quantitative (Math)

Example Question #91 : Expressions & Equations

Example Question #1 : How To Find Slope

Example Question #1 : Slope

Example Question #3 : How To Find Slope

Example Question #2 : Slope

Example Question #11 : How To Find Slope

Example Question #1 : How To Find X Or Y Intercept

Example Question #1 : How To Find X Or Y Intercept

Example Question #2 : How To Find X Or Y Intercept

All SSAT Upper Level Math Resources

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