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Intermediate Geometry : How to find out if lines are parallel

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Example Questions

Example Question #181 : Coordinate Geometry

Where do the lines y = 3x +4 and y-2 =3(x -3) intersect.

Possible Answers:

(1,3)

(3,2)

They never intersect.

(3,4)

(-4,3)

Correct answer:

They never intersect.

Explanation:

By solving both equations to standard form y=mx+b , you can see that both lines have the same slope, and therefore will never intersect.

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Example Question #1472 : Intermediate Geometry

A line passes through both the coordinates (1,2) and (7,-6) . A line passing through which other pair of coodinates would be parallel to this line?

Possible Answers:

(-5,-12) and (2,13)

(3,4) and (6,1)

(-3,0) and (0,-6)

(1,2) and (2,-4)

(-4,9) and (-1,5)

Correct answer:

(-4,9) and (-1,5)

Explanation:

The line has a slope of $-\frac{4}{3}$ , so you must find a pair of points which has the same slope.

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Example Question #12 : How To Find Out If Lines Are Parallel

Choose the equation that represents a line that is parallel to y=5x/7+2 .

Possible Answers:

-5x-7y+9=4

5x-7y+13=0

y=-7x/5+2

7x-5y-1=0

7y+5x=6

Correct answer:

5x-7y+13=0

Explanation:

Two lines are parallel if and only if they have the same slope. To find the slopes, we must put the equations into slope-intercept form, y=mx+b , where equals the slope of the line. In this case, we are looking for m=5/7 . To put 5x-7y+13=0 into slope-intercept form, we must subtract from each side of the equation, giving us -7y+13=-5x . We then subtract from each side, giving us -7y=-5x-13 . Finally, we divide both sides by , giving us y=5x/7+13/7 , which is parallel to y=5x/7+2 .

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Example Question #184 : Coordinate Geometry

Which of the following lines are parallel?

Possible Answers:

$y=\frac{1}{3}x-5$

y=-3x+5

None of these.

$y=\frac{1}{2}x-5$

y=2x+5

y=2x+7

y=-2x+7

y=3x-6

y=-3x+6

Correct answer:

None of these.

Explanation:

None of these lines are parallel.

In order for lines to be parallel, the lines must NEVER cross. Lines with identical slopes never cross. An example of two parallel lines would be:

y=3x-6

y=3x+6

Note that only the slope determines if line are parallel.

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Example Question #187 : Lines

Are the lines of the equations

$y = \frac{1}{2} x + 7$

and

2y = x + 7

parallel, perpendicular, or neither?

Possible Answers:

Neither

Perpendicular

Parallel

Correct answer:

Parallel

Explanation:

Write each equation in the slope-intercept form y = mx+b by solving for ; the -coefficient is the slope of the line.

The first equation,

$y = \frac{1}{2} x + 7$ ,

is in the slope-intercept form y = mx+b form. The slope is the -coefficient $\frac{1}{2}$ .

2y = x + 7 is not in this form, so it should be rewritten as such by multiplying both sides by $\frac{1}{2}$ :

$\frac{1}{2} \cdot 2y =\frac{1}{2} \cdot ( x + 7)$

$y =\frac{1}{2} \cdot x + \frac{1}{2} \cdot 7$

$y =\frac{1}{2} x + \frac{7}{2}$

The slope of the line of this equation is the -coefficient $\frac{1}{2}$ .

The lines of both equations have the same slope, $\frac{1}{2}$ , so it follows that they are parallel.

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Example Question #11 : How To Find Out If Lines Are Parallel

The slopes of two lines on the coordinate plane are 0.333 and $\frac{1}{3}$ .

True or false: the lines are parallel.

Possible Answers:

True

False

Correct answer:

False

Explanation:

Two lines are parallel if and only if they have the same slope. The slope of one of the lines is 0.333. The other line has slope $\frac{1}{3}$ , which is equal to 0.33333... ; this is not equal to 0.333. The two lines are not parallel.

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Example Question #191 : Lines

One line on the coordinate plane has its intercepts at (7, 0) and (0, 4) . A second line has its intercepts at (-4, 0) and (0, 7) . Are the lines parallel, perpendicular, or neither?

Possible Answers:

Perpendicular

Parallel

Neither

Correct answer:

Perpendicular

Explanation:

To answer this question, we must determine the slopes of both lines. If a line has as its intercepts (a, 0) and (0, b) , its slope is

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

The first line has as its slope

$m = -\frac{4}{7}$

The second line has as its slope

$m = -\frac{7}{-4} = \frac{7}{4}$

Two lines are parallel if and only if their slopes are equal; this is not the case.

They are perpendicular if and only if the product of their slopes is . The product of the slopes of the given lines is

$-\frac{4}{7} \cdot \frac{7}{4} = -1$ ,

so they are perpendicular.

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Example Question #12 : How To Find Out If Lines Are Parallel

The slopes of two lines on the coordinate plane are 0.75 and $\frac{3}{4}$ .

True or false: The lines are parallel.

Possible Answers:

False

True

Correct answer:

True

Explanation:

Two lines are parallel if and only if they have the same slope. The slope of one of the lines is $0.75 = \frac{75}{100}= \frac{3}{4}$ . The slope of the other is $\frac{3}{4}$ , so the lines have the same slope. The lines are parallel.

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Example Question #192 : Lines

A line which includes the point (6, 4) is parallel to the line with equation 4x+2y=15

Which of these points is on that line?

Possible Answers:

(9, -2)

(6, 2)

(5, 2)

(0, 7)

(10, 6)

Correct answer:

(9, -2)

Explanation:

Write the given equation in slope-intercept form:

4x+2y=15

2y=-4x+15

$\frac{1}{2}\cdot 2y=\frac{1}{2}\cdot \left (-4x \right )+\frac{1}{2}\cdot 15$

$y=-2x+\frac{15}{2}$

The given line has slope , so this is the slope of any line parallel to that line.

We can use the slope formula $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}}$ , testing each of our choices.

$(9, -2):\; m = \frac{4-(-2)}{6-9}}=\frac{6}{-3}=-2$

$(10, 6):\; m = \frac{4-6}{6-10}}=\frac{-2}{-4}=\frac{1}{2}$

$(5,2):\; m = \frac{4-2}{6-5}}=\frac{2}{1}=2$

$(6,2):\; m = \frac{4-2}{6-6}}=\frac{2}{0}$ , which is undefined

$(0, 7):\; m = \frac{4-7}{6-0}}=\frac{-3}{6}=-\frac{1}{2}$

The only point whose inclusion yields a line with slope is (9, -2) .

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Intermediate Geometry : How to find out if lines are parallel

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #181 : Coordinate Geometry

Example Question #1472 : Intermediate Geometry

Example Question #12 : How To Find Out If Lines Are Parallel

Example Question #184 : Coordinate Geometry

Example Question #187 : Lines

Example Question #11 : How To Find Out If Lines Are Parallel

Example Question #191 : Lines

Example Question #12 : How To Find Out If Lines Are Parallel

Example Question #192 : Lines

All Intermediate Geometry Resources

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