How to find the slope of parallel lines - Algebra

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Question

What is the slope of a line parallel to the line described by 3x + 8y =16?

Answer

First, you should put the equation in slope intercept form (y = _m_x + b), where m is the slope.

Isolate the y term

3x + 8y – 3x = 16 – 3x

8y = 16 – 3x

Rearrange terms

8y = –3x +16

Divide both sides by 8

$\frac{8y}{8}=\frac{(-3x+16)}{8}$

$y=-\frac{3}{8}x+2$

The slope of the line is -3/8. A parallel line will have the same slope, thus -3/8 is the correct answer.

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Question

Which equation described a line parallel to the line that connects points (–8,9) and (3,–4)?

Answer

In order for two lines to be parellel, their slopes have to be the same.

Find the slope of the line connecting those two points using the general slope formula, $m=\frac{y_2-y_1}{x_2-x_1}$ , where the points are and . In our case, the points are (–8,9) and (3,–4). The slope is calculated below.

$m=\frac{-4-9}{3-(-8)}=-\frac{13}{11}$

Match this slope value with one of the possible choice of equations. The correct equation is $y=-\frac{13}{11}(x-11)$ because its slope is the same.

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Question

What is the slope of a line parallel to $y=\frac{x}{2}+15$ ?

Answer

When two lines are parallel, they have the same slope. With this in mind we take the slope of the first line which is $\frac{1}{2}$ and make it the slope of our parallel line.

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

$y=(\frac{1}{2})x+15$

If , then $m=\frac{1}{2}$ .

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Question

What is the slope of a line that is parallel to ?

Answer

Parallel lines have identical slopes. To determine the slope of the given line, transform into the format, or $y=-\frac{3}{2}x+3$ . The slope of the given line is $-\frac{3}{2}$ , so its parallel line must also be $-\frac{3}{2}$ .

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Question

Which of the following are NOT parallel to each other?

Answer

Four of the answers are not in slope-intercept form.

For the lines to be parallel, all must share the same slopes.

To identify the slopes, this is the term of:

The only equation that does not have a slope of $-\frac{3}{2}$ is

$y=-\frac{2}{3}x+4$ .

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Question

Lines A and B are parallel. Line A can be represented by the equation .

Find the slope of line B.

Answer

If two lines are parallel, then they have the same slope.

Line A is:

Rewrite this in slope-intercept form where is the slope:

The slope of line A is .

If the slope of line A is , then the slope of line B must be .

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Question

Find the slope of a line parallel to the line with the equation:

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

And it has a slope of:

Parallel lines share the same slope.

The parallel line has a slope of .

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Question

Find the slope of a line parallel to the line with the equation:

$y=\frac{3}{4}x-10$

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$y=\frac{3}{4}x-10$

And it has a slope of:

$m=\frac{3}{4}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{3}{4}$ .

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Question

Find the slope of a line parallel to the line with the equation:

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

And it has a slope of:

Parallel lines share the same slope.

The parallel line has a slope of .

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Question

Find the slope of a line parallel to the line with the equation:

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

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

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

And it has a slope of:

$m=\frac{1}{2}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{1}{2}$ .

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Question

Find the slope of a line parallel to the line with the equation:

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

And it has a slope of:

Parallel lines share the same slope.

The parallel line has a slope of .

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Question

Find the slope of a line parallel to the line with the equation:

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

And it has a slope of:

Parallel lines share the same slope.

The parallel line has a slope of .

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Question

Find the slope of a line parallel to the line with the equation:

$y=\frac{3}{8}x-1$

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$y=\frac{3}{8}x-1$

And it has a slope of:

$m=\frac{3}{8}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{3}{8}$ .

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Question

Find the slope of a line parallel to the line with the equation:

$y=\frac{5}{6}x-12$

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$y=\frac{5}{6}x-12$

And it has a slope of:

$m=\frac{5}{6}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{5}{6}$ .

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Question

Find the slope of a line parallel to the line with the equation:

$y=\frac{2}{11}x-\frac{1}{4}$

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$y=\frac{2}{11}x-\frac{1}{4}$

And it has a slope of:

$m=\frac{2}{11}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{2}{11}$ .

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Question

Find the slope of a line parallel to the line with the equation:

$y=-\frac{8}{13}x+10$

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$y=-\frac{8}{13}x+10$

And it has a slope of:

$m=-\frac{8}{13}$

Parallel lines share the same slope.

The parallel line has a slope of $-\frac{8}{13}$ .

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Question

Find the slope of a line parallel to the line with the equation:

$y=\frac{12}{17}x-123$

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$y=\frac{12}{17}x-123$

And it has a slope of:

$m=\frac{12}{17}$

Parallel lines share the same slope.

The parallel line has a slope of $\frac{12}{17}$ .

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Question

Find the slope of a line parallel to the line with the equation:

Answer

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

And it has a slope of:

Parallel lines share the same slope.

The parallel line has a slope of .

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Question

If line X is parallel to line A with a slope of $\frac{7}{2}$ and a y-intercept of , what is the slope of line X?

Answer

By definition, lines are parallel if they have the same slope.

The problem states that line A has a slope of $\small \frac{7}{2}$ and that line X is parallel to it.

This means that line X must also have a slope of $\small \frac{7}{2}$ .

The y-intercept is not a determinant of lines being parallel or perpendicular.

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Question

If a line is parallel to the line , what must be the slope of the other line?

Answer

If a line is parallel to another line, they will never intersect. This means that their slopes will be the same.

The equation given is in standard form. Convert the equation to slope intercept form, , in order to determine the slope .

Subtract on both sides.

Simplify and reorganize the terms.

Divide by three on both sides.

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

Simplify both sides.

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

The slope of the parallel line must be $-\frac{1}{3}$ .

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