How to find the slope of parallel lines - Geometry

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Question

If the slope of line AB is 3_x_, and Angle 1 and Angle 8 are congruent, what is the slope of line CD, and why?

Answer

Angles 1 and 8 are a vertical pair. If these angles are congruent, it means that lines AB and CD are parallel based on the Vertical Angle Theorem. Parallel lines have the same slope, so the slope of CD is 3x.

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Question

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

Answer

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

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Question

Any line that is parallel to must have a slope of what?

Answer

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, , where equals the slope of the line. First, we must subtract from each side of the equation, giving us . Next, we divide both sides by , giving us . We can now see that the slope is .

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Question

Suppose the equation of the first line is . What must be the value of to make the second equation parallel to the first line?

Answer

Rewrite both equations so that they are in slope-intercept form, .

For the first equation:

The slope of the first line is .

Rewrite the second equation in slope-intercept form:

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

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Question

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?

Answer

Rewrite the equation of the first line in slope-intercept form, .

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

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

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

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

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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Question

Find a line parallel to the line with the equation:

Answer

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

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

Only the following line has the same slope:

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Question

Find a line parallel to the line with the equation:

Answer

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

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

Only the following line has the same slope:

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Question

Find a line parallel to the line with the equation:

Answer

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

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

Only the following line has the same slope:

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Question

Find a line parallel to the line with the equation:

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

Answer

For two lines to be parallel, they must have the same slope. For a line in , 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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Question

If the slope of line AB is 3_x_, and Angle 1 and Angle 8 are congruent, what is the slope of line CD, and why?

Answer

Angles 1 and 8 are a vertical pair. If these angles are congruent, it means that lines AB and CD are parallel based on the Vertical Angle Theorem. Parallel lines have the same slope, so the slope of CD is 3x.

Compare your answer with the correct one above

Question

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

Answer

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

Compare your answer with the correct one above

Question

Any line that is parallel to must have a slope of what?

Answer

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, , where equals the slope of the line. First, we must subtract from each side of the equation, giving us . Next, we divide both sides by , giving us . We can now see that the slope is .

Compare your answer with the correct one above

Question

Suppose the equation of the first line is . What must be the value of to make the second equation parallel to the first line?

Answer

Rewrite both equations so that they are in slope-intercept form, .

For the first equation:

The slope of the first line is .

Rewrite the second equation in slope-intercept form:

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

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Question

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?

Answer

Rewrite the equation of the first line in slope-intercept form, .

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

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

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

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

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.

Compare your answer with the correct one above

Question

Find a line parallel to the line with the equation:

Answer

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

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

Only the following line has the same slope:

Compare your answer with the correct one above

Question

Find a line parallel to the line with the equation:

Answer

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

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

Only the following line has the same slope:

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Question

Find a line parallel to the line with the equation:

Answer

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

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

Only the following line has the same slope:

Compare your answer with the correct one above

Question

Find a line parallel to the line with the equation:

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

Answer

For two lines to be parallel, they must have the same slope. For a line in , 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:

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

Compare your answer with the correct one above

Question

If the slope of line AB is 3_x_, and Angle 1 and Angle 8 are congruent, what is the slope of line CD, and why?

Answer

Angles 1 and 8 are a vertical pair. If these angles are congruent, it means that lines AB and CD are parallel based on the Vertical Angle Theorem. Parallel lines have the same slope, so the slope of CD is 3x.

Compare your answer with the correct one above

Question

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

Answer

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

Compare your answer with the correct one above

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