SSAT Upper Level Math : Coordinate Geometry

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

varsity tutors app store varsity tutors android store

Example Questions

Example Question #201 : Coordinate Geometry

Function 1

What equation is graphed in the above figure?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Ceiling function

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

Example Question #202 : Coordinate Geometry

Function

Give the equation graphed in the above figure.

Possible Answers:

\displaystyle y = |x+5|

\displaystyle y = |x| + 5

\displaystyle y = |x-5|

\displaystyle y = |5x|

\displaystyle y = |x| -5

Correct answer:

\displaystyle y = |x| + 5

Explanation:

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

Absolute value graph

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

Example Question #1 : How To Find Slope

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

Possible Answers:

\displaystyle -\frac{3}{4}

\displaystyle \frac{4}{3}

\displaystyle \frac{3}{4}

\displaystyle -\frac{4}{3}

Correct answer:

\displaystyle \frac{3}{4}

Explanation:

Use the following formula to find the slope:

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

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

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

Example Question #2 : How To Find Slope

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

Possible Answers:

\displaystyle -\frac{19}{3}

\displaystyle \frac{3}{19}

\displaystyle -\frac{3}{19}

\displaystyle \frac{19}{3}

Correct answer:

\displaystyle \frac{3}{19}

Explanation:

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

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

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

Example Question #3 : How To Find Slope

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

Possible Answers:

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

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

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

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

Correct answer:

\displaystyle \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.

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

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

Example Question #1 : Slope

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

Possible Answers:

\displaystyle 9

\displaystyle -\frac{4}{3}

\displaystyle \frac{5}{9}

\displaystyle \frac{9}{5}

Correct answer:

\displaystyle \frac{5}{9}

Explanation:

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

\displaystyle 5x-9y=12

\displaystyle -9y=-5x+12

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

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

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

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

Possible Answers:

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

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

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

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

Correct answer:

\displaystyle \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.

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

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

Example Question #91 : Expressions & Equations

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

Possible Answers:

\displaystyle \frac{3}{2}

\displaystyle -\frac{3}{2}

\displaystyle -\frac{3}{4}

\displaystyle \frac{3}{4}

Correct answer:

\displaystyle \frac{3}{2}

Explanation:

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

\displaystyle 12x-8y=6

Subtract \displaystyle 6 from either side:

\displaystyle 8y=12x-6

Divide each side by \displaystyle 8:

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

You can now easily identify the value of \displaystyle m.

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

Example Question #1 : How To Find Slope

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

Possible Answers:

\displaystyle -\frac{1}{4}

\displaystyle -4

\displaystyle \frac{1}{4}

\displaystyle 4

Correct answer:

\displaystyle -\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:

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

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

Example Question #1 : Slope

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

Possible Answers:

\displaystyle 3

\displaystyle -3

\displaystyle -6

\displaystyle \frac{1}{3}

\displaystyle 2

Correct answer:

\displaystyle \frac{1}{3}

Explanation:

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

\displaystyle 2x-6y=3

\displaystyle 2x=3+6y

\displaystyle 2x-3=6y

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

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

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

Learning Tools by Varsity Tutors