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Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : How To Find The Slope Of Parallel Lines

Find a line parallel to the line with the equation:

y=19x-14

Possible Answers:

y=-19x-2

$y=\frac{1}{19}x+14$

y=19x+2

y=14x+19

Correct answer:

y=19x+2

Explanation:

For two lines to be parallel, they must have the same slope. For a line in y=mx+b , or slope intercept form, corresponds to the slope of the line.

For the given line, m=19 . A line that is parallel must also then have the same slope.

Only the following line has the same slope:

y=19x+2

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Example Question #22 : Parallel Lines

Find a line parallel to the line with the equation:

y=129x-200

Possible Answers:

y=-129x+200

y=129x+41

$y=\frac{1}{129}x-2001$

y=200x-129

Correct answer:

y=129x+41

Explanation:

For two lines to be parallel, they must have the same slope. For a line in y=mx+b , or slope intercept form, corresponds to the slope of the line.

For the given line, m=129 . A line that is parallel must also then have the same slope.

Only the following line has the same slope:

y=129x+41

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Example Question #3 : How To Find The Slope Of Parallel Lines

Find a line parallel to the line with the equation:

$y=\frac{1}{365}x-2$

Possible Answers:

$y=-\frac{x}{365}+120$

y=365x-10

$y=\frac{x}{365}+4$

y=-25x+124

Correct answer:

$y=\frac{x}{365}+4$

Explanation:

For two lines to be parallel, they must have the same slope. For a line in y=mx+b , or slope intercept form, corresponds to the slope of the line.

For the given line, $m=\frac{1}{365}$ . A line that is parallel must also then have the same slope.

Only the following line has the same slope:

$y=\frac{x}{365}+4$

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

What is the equation of a line that is parallel to the line $\small y=\frac{1}{2}x+3$ and includes the point (4, 2) ?

Possible Answers:

$\small y=\frac{1}{2}x$

$\small y=2x-6$

$\small y=-2x+10$

$\small y=\frac{1}{2}x+6$

Correct answer:

$\small y=\frac{1}{2}x$

Explanation:

The line parallel to $\small y=\frac{1}{2}x+3$ must have a slope of $\frac{1}{2}$ , giving us the equation $\small y=\frac{1}{2}x+b$ . To solve for b, we can substitute the values for y and x.

$\small 2=(\frac{1}{2})(4)+b$

$\small 2=2+b$

$\small b=0$

Therefore, the equation of the line is $\small y=\frac{1}{2}x$ .

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Example Question #1 : How To Find The Equation Of A Parallel Line

Suppose a line y=2x . What is the equation of a parallel line that intersects point (1,3) ?

Possible Answers:

y=2x+5

y=2x+1

y=2x+3

y=2x+4

y=2x+2

Correct answer:

y=2x+1

Explanation:

A line parallel to y=2x must have a slope of two. Given the point (1,3) and the slope, use the slope-intercept formula to determine the -intercept by plugging in the values of the point and solving for :

y=mx+b

3=(2)(1)+b

3=2+b

3-2=2+b-2

b=1

Plug the slope and the -intercept into the slope-intercept formula:

y=2x+1

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Example Question #1 : How To Find The Equation Of A Parallel Line

Find the equation of the line parallel to 3x+3y=1 that passes through the point (2,2) .

Possible Answers:

y=x-2

y=3x-4

y=-x+4

y=3x+4

y=-x-4

Correct answer:

y=-x+4

Explanation:

Write 3x+3y=1 in slope intercept form, y=mx+b , to determine the slope, :

3y=-3x+1

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

The slope is:

m=-1

Given the slope, use the point (2,2) and the equation y=mx+b to solve for the value of the -intercept, . Substitute the known values.

2=(-1)(2)+b

b=4

With the known slope and the -intercept, plug both values back to the slope intercept formula. The answer is y=-x+4 .

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Example Question #1 : How To Find The Equation Of A Parallel Line

Given y=3x+20 , find the equation of a line parallel.

Possible Answers:

y=3x-12

$y=\frac{-1}{3}-20$

y=0.3x+20

y=-3x-12

$y=\frac{1}{3}x-20$

Correct answer:

y=3x-12

Explanation:

The definition of a parallel line is that the lines have the same slopes, but different intercepts. The only answer with the same slope is y=3x-12 .

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Example Question #32 : Parallel Lines

Which one of these equations is parallel to:

y=3x+4

Possible Answers:

y=3x+1

y=-3x+7

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

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

y=4

Correct answer:

y=3x+1

Explanation:

Equations that are parallel have the same slope.

For the equation:

y=3x+4

The slope is since that is how much changes with increment of .

The only other equation with a slope of is:

y=3x+1

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Example Question #1 : How To Find The Equation Of A Parallel Line

What equation is parallel to:

y=x

Possible Answers:

y=x+42746

y=2x

y=x^2+4

y=-x+1

y=0

Correct answer:

y=x+42746

Explanation:

To find a parallel line to

y=x

we need to find another equation with the same slope of or .

The only equation that satisfies this is y=x+42746 .

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Example Question #2 : How To Find The Equation Of A Parallel Line

What equation is parallel to:

y=5x+5

Possible Answers:

y=5x+10

y=x+5

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

y=4x+3

$y=\frac{1}{5}x+4$

Correct answer:

y=5x+10

Explanation:

To find an equation that is parallel to

y=5x+5

we need to find an equation with the same slope of .

Basically we are looking for another equation with .

The only other equation that satisfies this is

y=5x+10 .

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Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Slope Of Parallel Lines

Example Question #22 : Parallel Lines

Example Question #3 : How To Find The Slope Of Parallel Lines

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

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #32 : Parallel Lines

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #2 : How To Find The Equation Of A Parallel Line

All Intermediate Geometry Resources

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