Chapter 8.4, Problem 5C

To determine

To find:

The slope of the line that passes through the given points. Tell whether the slope is positive , negative , zero , or undefined .

Answer to Problem 5C

The slope of the linepassing through the given points would be 1 and hence positive.

Explanation of Solution

Given:

Two points on a line: $(2,3)\text{and (}4,5)$ .

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 $(2,3)=(x_1,y_1)\text{and (}4,5)=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{5-3}{4-2}\\ m=\frac{2}{2}\\ m=1\end{array}$

Therefore, the slope of the line passing through the given points would be1 and hence positive.