Chapter 13.2, Problem 23WE

To determine

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

Answer to Problem 23WE

The unknown $y$ coordinate is

  $y_2=6$

Explanation of Solution

Given:

A line with slope $\frac{3}{4}$ passes through points $\left(2,3\right)\text{ and }\left(10,?\right)$

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 $\left(2,3\right)\text{and }\left(10,?\right)$

Let the unknown $y$ coordinate be $y_2$

So,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ \frac{3}{4}=\frac{y_2-3}{10-2}\\ \frac{3}{4}=\frac{y_2-3}{8}\\ 24=4\left(y_2-3\right)\\ 24=4y_2-12\\ 4y_2=36\\ y_2=6\end{array}$

So, the unknown $y$ coordinate is

  $y_2=6$