Question

What is the slope of a line perpendicular to the line whose equation is 2x+2y=28

Answer 1

1

Explanation:

1) First, place the given equation in slope-intercept form (
`y = mx +b` format) to find its slope easier. Isolate the y:

`2x + 2y = 28\\2y = -2x + 28\\y = -x+14`

So, the equation of the line in slope-intercept form is
`y = -x + 14`. When an equation is in slope-intercept form, the
`m`, or the coefficient of the x-term, represents the slope. Thus, the slope for the given line would be -1.

2) Lines that are perpendicular have slopes that are opposite reciprocals of each other. We need to find the opposite reciprocal of -1, then.

To find the opposite reciprocal of a number, write the given number as a fraction first -- making -1 be written as
`-(1)/(1)` -- then switch the sign and flip the numerator and denominator. So, the opposite reciprocal of -1 is 1, and 1 is the slope of the perpendicular line.