Algebra - How to find out if lines are parallel

Which of the following lines is parallel to

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

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

Explanation

When comparing two lines to see if they are parallel, they must have the same slope. To find the slope of a line, we write it in slope-intercept form

where m is the slope.

The original equation

will need to be written in slope-intercept form. To do that, we will divide each term by 4

$\frac{4y}{4} = \frac{-2x}{4} + \frac{8}{4}$

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

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

Therefore, the slope of the original line is $-\frac{1}{2}$ . A line that is parallel to this line will also have a slope of $-\frac{1}{2}$ .

Therefore, the line

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

is parallel to the original line.

Find a line parallel to the line that has the equation:

$y=-\frac{1}{20}x-2$

Explanation

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

Only one of the choices also has the same slope and is the correct answer:

Which of the following lines is parallel to a line with the equation:

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

Explanation

For two lines to be parallel, they must have the same slope.

Lines can be written in the slope-intercept form:

In this equation, equals the slope and represents the y-intercept.

The slope of the given line is:

There is only one line with a slope of .

Find the equation of a line parallel to:

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

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

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

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

Explanation

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

In this equation, equals the slope and represents the y-intercept.

In the given equation:

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

Only one of the choices has a slope of $-\frac{3}{4}$ :

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

Find a line parallel to the line with the equation:

$y=\frac{4}{5}x-\frac{4}{5}$

$y=\frac{4}{5}x+12$

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

$y=\frac{4}{5}$

$y=\frac{5}{4}x+3$

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:

$m=\frac{4}{5}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\frac{4}{5}$ .

$y=\frac{4}{5}x+12$

Which of the following pairs of lines are parallel?

$y=\frac{1}{2}x-8$

Explanation

Lines can be written in the slope-intercept form:

In this form, equals the slope and represents where the line intersects the y-axis.

Parallel lines have the same slope: .

Only one choice contains tow lines with the same slope.

The slope for both lines in this pair is .

Find a line parallel to the line that has the equation:

$y=-\frac{12}{7}x-2$

$y=-\frac{12}{7}x-12$

$y=\frac{12}{7}x+12$

$y=\frac{7}{12}x-2$

Explanation

Lines can be written using the slope-intercept equation format:

Lines that are parallel have the same slope.

The given line has a slope of:

$m=-\frac{12}{7}$

Only one of the choices also has the same slope and is the correct answer:

$y=-\frac{12}{7}x-12$

Determine if the lines are parallel and find their slopes:

Explanation

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

Do that for each line:

$y-2x=3\rightarrow y=2x+3$

Both lines have a slope of 2 which makes them parallel.

Given the equations and , are the two lines parallel to each other?

Yes, the lines are parallel since slopes are alike.

$\textup{}$ No, the lines are NOT parallel since slopes are NOT alike.

$\textup{}$ Yes, the lines are parallel since y-intercepts are alike.

$\textup{}$ No, the lines are NOT parallel since y-intercepts are NOT alike.

$\textup{}$ Yes, the lines are parallel since slopes are NOT alike.

Explanation

For the lines to be parallel, both the lines must have similar slopes.

Write the slope-intercept form.

The represents the slope. Both of the equation have a slope of negative three. Therefore, both lines are parallel.

The answer is: $\textup{Yes, the lines are parallel since slopes are alike.}$

Which of the following lines is parallel to

$y = \frac{1}{7}x + 4$

Explanation

If two lines are parallel, then they have the same slope. To find the slope of a line, we write it in slope-intercept form

where m is the slope. So given the equation

we must solve for y. To do that, we will divide each term by 6. We get

$\frac{6y}{6} = \frac{-42x}{6} + \frac{18}{6}$

We can see the slope of this line is -7. Therefore, this line is parallel to the line

because it also has a slope of -7.

How to find out if lines are parallel

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