How to find the slope of parallel lines

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Math › How to find the slope of parallel lines

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

$\frac{1}{2}$

Explanation

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 .

Find a line parallel to the line with the equation:

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

Explanation

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:

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

$-\frac{3}{8}$

$-\frac{8}{3}$

$\frac{8}{3}$

$\frac{3}{8}$

Explanation

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.

Which of the following equations are parallel to ?

$y=\frac{2}{5}x+2$

$y=\frac{5}{2}x+2$

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

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

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

Explanation

For one equation to be parallel to another, the only requirement is that they must have the same slope. In order to figure out which answer choice is parallel to the given equation, you must first find the slope of the equation:

$y=\frac{2}{5}x-3$

From the simplified equation, you can see that the slope is $\frac{2}{5}$ .

The answer choice that has the same slope is $y=\frac{2}{5}x+2$ .

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

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

$\frac{1}{2}$

$-\frac{1}{2}$

Explanation

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 $\frac{1}{2}$ .

What is the slope of the line that runs through points $\left ( -10,5 \right )$ and $\left ( 4,-3 \right )$ ?

$-\frac{4}{7}$

$-\frac{9}{14}$

$\frac{7}{4}$

$\frac{4}{7}$

$\frac{14}{8}$

Explanation

Use the slope formula (difference between 's over difference between 's) to find that the slope is $-\frac{4}{}7$ .

Which of the following lines would be parallel to the line described by the equation?

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

$y=-\frac{1}{2}x-9$

Explanation

The way to determine parallel lines is to look at the slope. That means when you look at the equation in slope-intercept form, , you're looking at the .

In the given problem, the slope is . Parallel lines will have identical slopes; thus, any line that is parallel to the line described by the equation would ALSO have a slope of . Only one answer choice satisfies that requirement:

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

$\frac{1}{9}$

$-\frac{1}{9}$

Explanation

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 .

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

$\frac{1}{2}$

Explanation

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.