Exercise 32 Page 176

We are given an incorrect solution and asked to find the error that was made. First we will calculate the slope and check whether it was done correctly. Let's substitute the points $(1,2)$ and $(4,3)$ into the Slope Formula The slope was determined correctly. The error must have been made when using the formula. Let's recall the point-slope form. In this step we need to substitute the slope and one of the points into the formula. We can do this with either of our points, giving us two possibilities.

Point	Slope	$y-y_1=m(x-x_1)$
$(1,2)$	$\frac{1}{3}$	$y-2=\frac{1}{3}(x-1)$
$(4,3)$	$\frac{1}{3}$	$y-3=\frac{1}{3}(x-4)$

When writing the point-slope form one point must be substituted into the formula. We can see that the first point's $y\text{-}$value and the second point's $x\text{-}$value were used. This is incorrect, as the coordinates must be from the same point.