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SAT Math : How to find out if lines are parallel

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Example Questions

Example Question #411 : Geometry

Which of the following are parallel to the line y=2x-2 ?

A. y=2x-12

B. y=-2x-2

C. $y=-\frac{1}{2}x+2$

D. y=2x-6

E. $y=-\frac{1}{2}x +6$

Possible Answers:

D & E

A, B, & C

A & D

C & D

None of the given answers

Correct answer:

A & D

Explanation:

In order for two lines to be parallel, they must have the same slope and different y-intercepts. In slope-intercept form, the slope of the coefficient of our value.

We want to find lines that have a slope of . The two answers that share this slope with the given equation are y=2x-12 and y=2x-6 , which correspond with answers A and D.

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Example Question #31 : Coordinate Geometry

Given lines on the coordinate plane as follows:

Line A has equation 2x+7y = 13

Line B has equation 7x-2y = 13

Line C has equation 2x-7y = 13

Which of the following is a true statement?

Possible Answers:

Line A, Line B, and Line C are parallel to one other.

No two of Line A, Line B, and Line C are parallel to each other.

Line A and Line B are parallel to each other, but Line C is parallel to neither Line A nor Line B.

Line B and Line C are parallel to each other, but Line A is parallel to neither Line B nor Line C.

Line A and Line C are parallel to each other, but Line B is parallel to neither Line A nor Line C.

Correct answer:

No two of Line A, Line B, and Line C are parallel to each other.

Explanation:

Two lines are parallel if and only if they have the same slope. Therefore, we must find the slope of each line. We do this by rewriting each equation in slope-intercept form y = mx +b , with -coefficient being the slope of the line.

In each case, solve for by isolating this variable on the left side.

Line A:

2x+7y = 13

2x+7y - 2x = 13 - 2x

7y = - 2x + 13

$\frac{7y }{7}=\frac{ - 2x + 13}{7}$

$y=-\frac{ 2} {7} x + \frac{13}{7}$

The slope of Line A is the -coefficient $m=-\frac{ 2} {7}$ .

Line B:

7x-2y = 13

7x-2y - 7x = 13 - 7x

-2y = - 7x + 13

$\frac{-2y }{-2}=\frac{ - 7x + 13}{-2}$

$y= \frac{7} { 2} x- \frac{13}{2}$

The slope of Line Bis the -coefficient $m= \frac{7}{ 2}$ .

Line C:

2x-7y = 13

2x-7y - 2x = 13 - 2x

-7y = - 2x + 13

$\frac{-7y }{-7}=\frac{ - 2x + 13}{-7}$

$y= \frac{ 2} {7} x- \frac{13}{7}$

The slope of Line C is the -coefficient $m= \frac{ 2} {7}$ .

No two of the given lines have the same slope, so no two are parallel.

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Example Question #33 : Parallel Lines

Given Lines A, B, and C on the coordinate plane as follows:

The equation of Line A is y = 3x+ 17 .

The equation of Line B is -9x + 3y =17 .

The equation of Line C is 6x - 2y = 17 .

Which of the following is a true statement?

Possible Answers:

No two of Line A, Line B, and Line C are parallel to each other.

Line A and Line C are parallel to each other, but Line B is parallel to neither Line A nor Line C.

Line A, Line B, and Line C are parallel to one other.

Line A and Line B are parallel to each other, but Line C is parallel to neither Line A nor Line B.

Line B and Line C are parallel to each other, but Line A is parallel to neither Line B nor Line C.

Correct answer:

Line A, Line B, and Line C are parallel to one other.

Explanation:

In each case, solve for by isolating this variable on the left side.

Line A:

y = 3x+ 17 .

This equation is already in slope-intercept form. The slope of Line A is the -coefficient m = 3 .

Line B:

-9x + 3y =17

-9x + 3y+ 9x =17 + 9x

3y = 9x + 17

$\frac{3y}{3} =\frac{ 9x + 17 }{ 3 }$

$y = 3x + \frac{17}{3}$

The slope of Line B is the -coefficient m = 3 .

Line C:

6x - 2y = 17

6x - 2y - 6x = 17- 6x

- 2y = - 6x + 17

$\frac{- 2y}{-2} =\frac{ - 6x + 17}{-2}$

$y =3x - \frac{ 17}{2}$

The slope of Line C is the -coefficient m = 3 .

In each case, the slope is m = 3 . The three lines, having the same slope, are all parallel to one another.

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Example Question #34 : Parallel Lines

Given Lines A, B, and C on the coordinate plane as follows:

Line A has intercepts (0,4) and (6,0) .

Line B has intercepts (0, -6 ) and (9,0) .

Line C has intercepts (0, -8) and (-12, 0) .

Which statement is true?

Possible Answers:

Lines A and B are parallel to each other, but Line C is parallel to neither line.

Lines A, B, and C are all parallel to one another.

Lines A and C are parallel to each other, but Line B is parallel to neither line.

Lines B and C are parallel to each other, but Line A is parallel to neither line.

No two of Lines A, B, and C are parallel.

Correct answer:

Lines A and C are parallel to each other, but Line B is parallel to neither line.

Explanation:

Two lines are parallel if an only if their slopes are equal. The slope of a line with -intercept (a,0) and -intercept (0, b) can be determined using the formula

$m = -\frac{b}{a}$ .

Calculate the slope of Line A by setting a = 6, b= 4 :

$m_{A} = -\frac{4}{6} = -\frac{2}{3}$

Calculate the slope of Line B by setting a = 9, b= -6 :

$m_{B} = -\frac{-6}{9} = \frac{2}{3}$

Calculate the slope of Line B by setting a =-12, b= -8 :

$m_{C} = -\frac{-8}{-12} =- \frac{2}{3}$

Lines A and C have the same slope and are parallel; Line B has a different slope and is not parallel to the other two.

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Example Question #2 : How To Find Out If Lines Are Parallel

Which of the following lines is parallel to:

4y-12x=2

Possible Answers:

x-3y=9

x+4y=10

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

$x-\frac{1}{3}y=7$

Correct answer:

$x-\frac{1}{3}y=7$

Explanation:

First write the equation in slope intercept form. Add 12x to both sides to get 4y = 12x + 2 . Now divide both sides by to get y = 3x + 0.5 . The slope of this line is , so any line that also has a slope of would be parallel to it. The correct answer is $x - \frac{1}{3}y = 7$ .

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SAT Math : How to find out if lines are parallel

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #411 : Geometry

Example Question #31 : Coordinate Geometry

Example Question #33 : Parallel Lines

Example Question #34 : Parallel Lines

Example Question #2 : How To Find Out If Lines Are Parallel

All SAT Math Resources

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