Chapter 8.1, Problem 26PSC

To determine

To find: The slope of the lineand the coordinates of points using the given equation and points.

Answer to Problem 26PSC

Points are: (6, 12) and (10, 22)

Slope of the line:3

Explanation of Solution

Given information The equation of line: $\text{y =}\frac{5}{2}\text{x}-3$

Passing through points whose x − coordinates are 6 and 10

Formula used

For finding y − coordinates, put the values of x − coordinate in the given line equation and

For finding slope of the line: divide the difference of y − coordinates by difference of x - coordinates

Calculation Put x =6 in the given line equation,

  $\text{y =}\frac{5}{2}\text{x}-3$ , we get

  $\begin{array}{l}\text{y }\\ \text{=}\frac{5}{2}\text{x}-3\\ =\frac{5}{2}\times \text{6}-3\\ =5\times 3-3\\ =15-3\\ =12\end{array}$

Therefore,

First point: (6, 12)

Put x =10 in the given line equation,

  $\text{y =}\frac{5}{2}\text{x}-3$ , we get

  $\begin{array}{l}\text{y }\\ \text{=}\frac{5}{2}\text{x}-3\\ =\frac{5}{2}\times 10-3\\ =5\times 5-3\\ =25-3\\ =22\end{array}$

Therefore,

Second point: (10, 22)

Slope of the line

= $\begin{array}{l}=\frac{22-10}{10-6}\\ =\frac{12}{4}\\ =3\end{array}$