Question

2x+8y=4 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 8y = 4 into this form

Subtract 2x from both sides

8y = - 2x + 4 ( divide all terms by 8 )

y = -
`(1)/(4)` x +
`(1)/(2)` ← in slope- intercept form

with slope m = -
`(1)/(4)`

• Parallel lines have equal slopes, thus

slope of parallel line = -
`(1)/(4)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(4) )` = 4

Answer 2

Let's solve for x.

2x+8y=4

Step 1: Add -8y to both sides.

2x+8y+−8y=4+−8y

2x=−8y+4

Step 2: Divide both sides by 2.

2x/2

=

−8y+4/2

=−4y+2

Answer:

x=−4y+2