Chapter 8.4, Problem 3E

To determine

To describe and correct:

The error in calculating the slope of the line through the points (5,4) and (0,2).

Answer to Problem 3E

The slope of the line passing through the given points would be $\frac{2}{5}$ .

Explanation of Solution

Given:

An error while calculating the slope between the points (5,4) and (0,2).

Concept used:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1},\text{where,}\\ m=\text{Slope of line,}\\ y_2-y_1=\text{Difference between two }y\text{-coordinates}\\ x_2-x_1=\text{Difference between two }x\text{-coordinates of same }y-\text{coordinates}\end{array}$

Calculation:

Let point $(5,4)=(x_1,y_1)\text{and (}0,2)=(x_2,y_2)$ .

Upon looking at our given steps, we can see that the x -coordinates of points are interchanged in slope formula, that is $x_1$ is substituted in place of $x_2$ .

Upon substituting coordinates of our given points in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{2-4}{0-5}\\ m=\frac{-2}{-5}\\ m=\frac{2}{5}\end{array}$

Therefore, the slope of the line passing through the given points would be $\frac{2}{5}$ .