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

We use the point slope form of the equation

y - y1 = m(x - x1)

We need the slope. The information we are given tells us the line is parallel to the line whose equation is

x + y = 3

Unfortunately, this equation is not in slope-intercept form. To put it into slope intercept form, we solve for y

y = -x + 3

When the equation of the line is solved for y, the slope is the coefficient of the x term which in this case is -1. So

m = -1.

We are given the point

(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 + 5