Question

HELP PLEASE!!
Use the point and the slope to graph each line. Write the equation of the line

Answer 1

WHAT DO WE KNOW ABOUT PERPENDICULAR LINES ?

IS THAT WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE A PRODUCT OF -1.

TO FIND THE GRADIENT OF THE LINE PERPENDICULAR TO THE LINE WITH SLOPE/GRADIENT -1 WE CAN SAY

`m1 * m2 = - 1 \\ - 1 * m2 = - 1 \\ m2 = 1`

THIS MEANS THAT THE GRADIENT OF THE NEW LINE IS 1

the general equation of the straight line is y=mx+c

`- 2 = 1(2) + c \\ - 2 = 2 + c \\ c = - 2 - 2 \\ c = - 4`

This means that

`y = 1x - 4 \\ simply \\ y = x - 4`

Answer 2

y = x in the slope intercept form

y - 2 = 1(x -2) in the point-slope form of a line

Explanation:

Perpendicular slopes are opposite reciprocals of each other. So the perpendicular slope would be 1.

We could write this in the point slope form of a line and the answer would be:

y - 2 = 1(x -2) This would be the point slope form of a line.

If you want your answer in the slope intercept form

y -2 = 1(x-2)

y - 2 = x - 2 Add two to both sides

y = x