4. Find the equation of the line that goes through the point (2, 3) perpendicular to the line whose equation is x + y = 3.

We use the point slope form of the equation

y - y1 = m(x - x1)

In problem 2, we sqaw that the slope of the line whose equation is x + y = 3 was -1. The slope of a perpendicular line would be the negative reciprocal of that or

m = 1

As with problem 2, the point on the line is

(x1, y1) = (2, 3)

We put this into the point slope form of the equation

y - y1 = m(x - x1)

y - 3 = (x - 2)

This can be simplified if we solve for y

y - 3 = x - 2

y = x - 2 + 3

y = x + 1