Which of the following equations contains the point (-4, 0) and is parallel to the line y = -4x + 1?

Q: How do you find an equation with a point and a parallel line?

To find a line thats parallel to a line and goes through a particular point, use the points coordinates for (x1, y1) in point slope form: y - y1 = m (x - x1). Then, just plug the old lines slope in for m!

Algebra 1 parallel and perpendicular lines

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Algebra Examples
Parallel Lines
Vertical Lines
Not The Same Line
Example: is y = 3x + 2 parallel to y − 2 = 3x ?
Perpendicular Lines
Quick Check of Perpendicular
Vertical Lines
How do you find an equation with a point and a parallel line?
Which like is parallel to the line y − 4x − 1?
What is the equation for line Y 4x?
How do you find an equation that is parallel?

Jio O.

asked • 07/23/18

i want to know what equation contains the point (-4,0) and the equation parallel to the line y=-4x+1

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1 Expert Answer

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Arthur D. answered • 07/23/18

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parallel lines have the same slope

y=-4x+1

y=mx+b

y=-4x+b

use the point (-4,0)

0=(-4)(-4)+b

0=16+b

b=-16

the equation of the line is y=-4x-16

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Algebra Examples

Find Any Equation Parallel to the Line y=4x-1

Choose a point that the parallel line will pass through.

Use the slope-intercept form to find the slope.

The slope-intercept form is , where is the slope and is the y-intercept.

Using the slope-intercept form, the slope is .

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .

Simplify the equation and keep it in point-slope form.

How to use Algebra to find parallel and perpendicular lines.

Parallel Lines

How do we know when two lines are parallel?

Their slopes are the same!

Example:

Find the equation of the line that is:

parallel to y = 2x + 1
and passes though the point (5,4)

The slope of y=2x+1 is: 2

The parallel line needs to have the same slope of 2.

We can solve it using the "point-slope" equation of a line:

y − y1 = 2(x − x1)

And then put in the point (5,4):

y − 4 = 2(x − 5)

And that answer is OK, but let's also put it in y = mx + b form:

y − 4 = 2x − 10

y = 2x − 6

Vertical Lines

But this does not work for vertical lines ... I explain why at the end.

Not The Same Line

Be careful! They may be the same line (but with a different equation), and so are not parallel.

How do we know if they are really the same line? Check their y-intercepts (where they cross the y-axis) as well as their slope:

Example: is y = 3x + 2 parallel to y − 2 = 3x ?

For y = 3x + 2: the slope is 3, and y-intercept is 2

For y − 2 = 3x: the slope is 3, and y-intercept is 2

In fact they are the same line and so are not parallel

Perpendicular Lines

Two lines are Perpendicular when they meet at a right angle (90°).

To find a perpendicular slope:

When one line has a slope of m, a perpendicular line has a slope of −1m

In other words the negative reciprocal

Example:

Find the equation of the line that is

perpendicular to y = −4x + 10
and passes though the point (7,2)

The slope of y=−4x+10 is: −4

The negative reciprocal of that slope is:

m = −1−4 = 14

So the perpendicular line will have a slope of 1/4:

y − y1 = (1/4)(x − x1)

And now put in the point (7,2):

y − 2 = (1/4)(x − 7)

And that answer is OK, but let's also put it in "y=mx+b" form:

y − 2 = x/4 − 7/4

y = x/4 + 1/4

Quick Check of Perpendicular

When we multiply a slope m by its perpendicular slope −1m we get simply −1.

So to quickly check if two lines are perpendicular:

When we multiply their slopes, we get −1

Like this:

Are these two lines perpendicular?

Line	Slope
y = 2x + 1	2
y = −0.5x + 4	−0.5

When we multiply the two slopes we get:

2 × (−0.5) = −1

Yes, we got −1, so they are perpendicular.

Vertical Lines

The previous methods work nicely except for a vertical line:

In this case the gradient is undefined (as we cannot divide by 0):

m = yA − yBxA − xB = 4 − 12 − 2 = 30 = undefined

So just rely on the fact that:

a vertical line is parallel to another vertical line.
a vertical line is perpendicular to a horizontal line (and vice versa).

Summary

parallel lines: same slope
perpendicular lines: negative reciprocal slope (−1/m)

How do you find an equation with a point and a parallel line?

To find a line that's parallel to a line and goes through a particular point, use the point's coordinates for (x1, y1) in point slope form: y - y1 = m (x - x1). Then, just plug the old line's slope in for m!

Which like is parallel to the line y − 4x − 1?

All lines that are parallel to y=−4x−1 y = - 4 x - 1 have the same slope of −4 .

What is the equation for line Y 4x?

The line y = 4x has a slope of 4 and an intercept of zero (there is no "b" in the standard equation y = mx + b). The slope (m = 4) will be the same slope as any parallel line. Parallel lines will all have the same slope.

How do you find an equation that is parallel?

Parallel lines have the same slope and differing y-intercepts. Since \displaystyle y = 9x + 5 is the only equation with the same slope, and the y-intercept is different, this is the equation of the parallel line.