Question

Enter the equation of the line in slope-intercept form. Enter the answer in fraction form.

5
The line perpendicular to y = -x +5 that passes through (5, -1).
The equation of the line that passes through (5, -1) is y =

Answer 1

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

We have the following line:

`y = -x + 5`

The slope is
`m_ {1} = - 1`

We find
`m_ {2} = \frac {-1} {m_ {1}} = \frac {-1} {- 1} = 1`

Thus, the equation of the perpendicular line is of the form:

`y = x + b`

We substitute the point
`(x, y) :( 5, -1)`and find "b":

`-1 = 5 + b\\-1-5 = b\\-6 = b`

Finally, the equation is:

`y = x-6`

Answer:

`y = x-6`