Chapter 13.2, Problem 25WE

To determine

To find unknown $y$ coordinate of one of point .

Answer to Problem 25WE

The unknown $y$ coordinate is

  $y_2=mr-mp+q$

Explanation of Solution

Given:

A line with slope $m$ passes through points $\left(p,q\right)\text{ and }\left(r,?\right)$

Calculation:

Slope of a line when two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given is

  $m=\frac{y_2-y_1}{x_2-x_1}$

Points given are $\left(p,q\right)\text{ and }\left(r,?\right)$

Let the unknown $y$ coordinate be $y_2$

So,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{y_2-q}{r-p}\\ y_2-q=m\left(r-p\right)\\ y_2=m\left(r-p\right)+q\\ y_2=mr-mp+q\end{array}$

So, the unknown $y$ coordinate is

  $y_2=mr-mp+q$