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Intermediate Geometry : Intermediate Geometry

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

Transverselinestilted

The slope of line CD is 4x, and Angle 1 and Angle 5 are congruent. What is the slope of line AB and why?

Possible Answers:

There is not enough information to determine

4x, because of Corresponding Angles Theorem

4x, because of the Vertical Angle Theorem

4x, because of Alternate Interior Angles Theorem

(1/4)x, because of the Corresponding Angle Theorem

Correct answer:

4x, because of Corresponding Angles Theorem

Explanation:

Parallel lines have the same slope. If Angles 1 and 5 are congruent, then lines AB and CD have the same slope (4x) based on the Congruent Angles Theorem.

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Example Question #2 : How To Find The Slope Of Parallel Lines

Any line that is parallel to 6x-2y=4 must have a slope of what?

Possible Answers:

1/3

-1/3

Correct answer:

Explanation:

Two lines are parallel if and only if they have the same slope. To find the slope, we must put the equation into slope-intercept form, y=mx+b , where equals the slope of the line. First, we must subtract from each side of the equation, giving us -2y=-6x+4 . Next, we divide both sides by , giving us y=3x-2 . We can now see that the slope is .

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Example Question #1481 : Intermediate Geometry

Suppose the equation of the first line is -3x+y=4 . What must be the value of to make the second equation -kx=4+y parallel to the first line?

Possible Answers:

$-\frac{3}{4}$

$\frac{4}{3}$

$\frac{3}{4}$

Correct answer:

Explanation:

Rewrite both equations so that they are in slope-intercept form, y=mx+b .

For the first equation:

-3x+y=4

y=3x+4

The slope of the first line is .

m=3

Rewrite the second equation in slope-intercept form:

-kx=4+y

-kx -4=y

The value of must be equal to three to be parallel. Solve for .

-k=3

k=-3

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

If the equation of one line is $\frac{1}{10}x-10y = 1$ , what must be the slope of another line so that both lines are parallel to each other?

Possible Answers:

$\frac{1}{100}$

$\frac{1}{10}$

$-\frac{1}{100}$

Correct answer:

$\frac{1}{100}$

Explanation:

Rewrite the equation of the first line in slope-intercept form, y=mx+b .

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

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

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

$y=\frac{1}{100}x -\frac{1}{10}$

The value of the slope, , can be seen as $\frac{1}{100}$ . For another line to be parallel to this line, their slopes must be the same.

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Example Question #2 : How To Find The Slope Of Parallel Lines

Find a line parallel to the line with the equation:

y=10x-2

Possible Answers:

$y=-\frac{1}{10}x+2$

y=-10x-2

y=10x+14

$y=\frac{1}{10}x-2$

Correct answer:

y=10x+14

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=10 . A line that is parallel must also then have the same slope.

Only the following line has the same slope:

y=10x+14

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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=19x-14

Possible Answers:

y=-19x-2

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

y=14x+19

y=19x+2

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 #4 : How To Find The Slope Of Parallel Lines

Find a line parallel to the line with the equation:

y=129x-200

Possible Answers:

y=129x+41

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

y=-129x+200

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 #9 : 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=365x-10

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

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

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 #2 : 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:

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

$\small y=2x-6$

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

$\small y=-2x+10$

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+1

y=2x+4

y=2x+3

y=2x+5

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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Intermediate Geometry : Intermediate Geometry

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 #2 : How To Find The Slope Of Parallel Lines

Example Question #1481 : Intermediate Geometry

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

Example Question #2 : How To Find The Slope Of Parallel Lines

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

Example Question #4 : How To Find The Slope Of Parallel Lines

Example Question #9 : How To Find The Slope Of Parallel Lines

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

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

All Intermediate Geometry Resources

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