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SSAT Upper Level Math : Equations of Lines

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 #1 : Equations Of Lines

Give the equation of a line that passes through the point (4,7) and has slope 1.

Possible Answers:

x + y = 11

x = 4

x-y = 3

x-y = -3

y = 7

Correct answer:

x-y = -3

Explanation:

We can use the point slope form of a line, substituting $m = 1, x_{1} = 4, y _{1} = 7$ .

$y- y_{1} = m (x-x_{1})$

y- 7 = 1 (x-4)

y- 7 = x-4

y- 7 -y +4 = x-4 -y +4

-3 = x-y

x-y = -3

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Example Question #2 : Equations Of Lines

A line can be represented by 2x+3y=6 . What is the slope of the line that is perpendicular to it?

Possible Answers:

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

You will first solve for Y, to get the equation in y=mx+b form.

represents the slope of the line, which would be $-\frac{2}{3}$ .

A perpendicular line's slope would be the negative reciprocal of that value, which is $\frac{3}{2}$ .

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

Find the equation the line goes through the points (3,4) and (0,2) .

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

First, find the slope of the line.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{0-3}=\frac{-2}{-3}=\frac{2}{3}$

Now, because the problem tells us that the line goes through (0,2) , our y-intercept must be .

Putting the pieces together, we get the following equation:

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

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Example Question #3 : Equations Of Lines

A line passes through the points (-4, 6) and (-2, -2) . Find the equation of this line.

Possible Answers:

y=-4x-10

$y=\frac{1}{4}x-8$

$y=-\frac{1}{4}x+10$

y=4x+10

Correct answer:

y=-4x-10

Explanation:

To find the equation of a line, we need to first find the slope.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-6}{-2-(-4)}=\frac{-8}{2}=-4$

Now, our equation for the line looks like the following:

y=-4x+b

To find the y-intercept, plug in one of the given points and solve for . Using (-4, 6) , we get the following equation:

6=-4(-4)+b

Solve for .

6=16+b

b=-10

Now, plug the value for into the equation.

y=-4x-10

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Example Question #4 : Equations Of Lines

What is the equation of a line that passes through the points (8,1) and (-2, -7) ?

Possible Answers:

$y=\frac{5}{4}x+\frac{32}{5}$

$y=-\frac{4}{5}x+\frac{27}{5}$

$y=\frac{4}{5}x-\frac{27}{5}$

$y=\frac{27}{5}x-\frac{4}{5}$

Correct answer:

$y=\frac{4}{5}x-\frac{27}{5}$

Explanation:

First, we need to find the slope of the line.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-1}{-2-8}=\frac{-8}{-10}=\frac{4}{5}$

Next, find the -intercept. To find the -intercept, plug in the values of one point into the equation y=mx+b , where is the slope that we just found and is the -intercept.

$1=8(\frac{4}{5})+b$

Solve for .

$1=\frac{32}{5}+b$

$b=-\frac{27}{5}$

Now, put the slope and -intercept together to get $y=\frac{4}{5}x-\frac{27}{5}$

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Example Question #4 : Equations Of Lines

Lines

Examine the above diagram. What is x + y ?

Possible Answers:

125

145

135

Correct answer:

125

Explanation:

Use the properties of angle addition:

$\left ( x - 13\right )+ (y + 25) +43= 180$

x + y + 25+43- 13= 180

x + y + 55= 180

x + y + 55-55= 180-55

x + y = 125

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Example Question #5 : Equations Of Lines

Are the following two equations parallel?

y=2x+13

5y=10x+95

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

When two lines are parallal, they must have the same slope.

Look at the equations when they are in slope-intercept form, y=mx+b where b represents the slope.

We must first reduce the second equation since all of the constants are divisible by .

This leaves us with y=2x+19 . Since both equations have a slope of , they are parallel.

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Example Question #192 : Algebra

Reduce the following expression:

$\frac{10a^{3}b^{5}c^{-2}}{2a^{2}}$

Possible Answers:

$\frac{5ab^{3}}{c^{2}}$

$10a^{1.5}b^{5}c^{2}$

$\frac{5a^{5}b^{5}}{c^{2}}$

$10a^{1.5}b^{-5}c^{2}$

$\frac{5ab^{5}}{c^{2}}$

Correct answer:

$\frac{5ab^{5}}{c^{2}}$

Explanation:

For this expression, you must take each variable and deal with them separately.

First divide you two constants 10/2=5 .

Then you move onto and when you divide like exponents you must subtract the exponents leaving you with .

is left by itself since it is already in a natural position.

Whenever you have a negative exponential term, you must it in the denominator.

This leaves the expression of $\frac{5ab^{5}}{c^{2}}$ .

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Example Question #6 : Equations Of Lines

Give the equation of a line that passes through the point (4,7) and has an undefined slope.

Possible Answers:

y = 4

y = 7

x + y = 11

x = 4

x = 7

Correct answer:

x = 4

Explanation:

A line with an undefined slope has equation x = a for some number ; since this line passes through a point with -coordinate 4, then this line must have equation x = 4

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Example Question #7 : How To Find The Equation Of A Line

Give the equation of the line through (2,9) and (8,1) .

Possible Answers:

4x-3y=29

3x-4y=20

4x+3y=35

-3x+4y=30

3x+4y=28

Correct answer:

4x+3y=35

Explanation:

First, find the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{9-1}{2-8}=\frac{8}{-6}=-\frac{4}{3}$

Apply the point-slope formula:

$y-y_{1}= m (x-x_{1})$

$y-1= -\frac{4}{3} (x-8)$

$y-1= -\frac{4}{3} x- \left (-\frac{4}{3} \right )8$

$y-1= -\frac{4}{3} x+ \frac{32}{3}$

$y= -\frac{4}{3} x+ \frac{35}{3}$

Rewriting in standard form:

$\frac{4}{3} x + y= \frac{35}{3}$

4x+3y=35

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SSAT Upper Level Math : Equations of Lines

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Equations Of Lines

Example Question #2 : Equations Of Lines

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

Example Question #3 : Equations Of Lines

Example Question #4 : Equations Of Lines

Example Question #4 : Equations Of Lines

Example Question #5 : Equations Of Lines

Example Question #192 : Algebra

Example Question #6 : Equations Of Lines

Example Question #7 : How To Find The Equation Of A Line

All SSAT Upper Level Math Resources

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