Question

What is the equation of the line in slope-intercept form? the line perpendicular to y = x + 2 through (-7, -8)​

Answer 1

`y=-x-15`

Explanation:

Point-slope formula:
`y-y_1=m(x-x_1)`, where
`(x_1, \ y_1)` are the coordinates of a point on the line, and
`m` is the slope of the line.

You are given a point that the line you are trying to find passes through, and a slope. The slope is less obvious than the point, but you can find the slope using the given information.

The line perpendicular to y = x + 2 will have the opposite reciprocal slope of this line. The slope of y = x + 2 is 1, so the opposite reciprocal of 1 is:

• 
  `m=-(1)/(1) =-1`

Now that you have both a point and the slope of the line you are trying to find, you can substitute these values into the point-slope formula (Notice: the name of this formula contains both "point" and "slope").

Substitute
`(-7, \ -8)` for
`(x_1,\ y_1)` and
`m=-1` into the point-slope formula.

• 
  `y-(-8)=-1(x-(-7))`

Simplify this equation.

• 
  `y+8=-1(x+7)`

Distribute -1 inside the parentheses.

• 
  `y+8=-x-7`

Subtract 8 from both sides of the equation.

• 
  `y=-x-15`

This line is in slope-intercept form (
`y=mx+b`), so we are done.