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What is the slope of the line that passes through (2,1) and (7,-2)? 1. \frac{5}{3} \\2....

Question:

What is the slope of the line that passes through (2,1) and (7,-2)?

{eq}1. \frac{5}{3} \\2. \frac{-1}{3} \\3. \frac{-3}{5} \\4. \frac{1}{5} {/eq}

Slope of a Line:

The slope of a line is by how much the line is rising according to the run. The slope of a line that passes through the points {eq}(x_1, y_1) {/eq} and {eq}(x_2, y_2) {/eq} is given by:

$$m= \dfrac{y_2-y_1}{x_2-x_1} $$

This is obtained by taking the ratio of differences of y coordinates and x coordinates.

Answer and Explanation:

The given points are:

$$(x_1, y_1)=(2, 1) \\ (x_2, y_2)= (7, -2) $$

The slope of the line is calculated using:

$$\begin{align} m&= \dfrac{y_2-y_1}{x_2-x_1} \\ &= \dfrac{-2-1}{7-2} \\ &= \boxed{\mathbf{\dfrac{-3}{5}}} \end{align} $$

Therefore, the answer is option (3).


Learn more about this topic:

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How to Find and Apply The Slope of a Line

from ELM: CSU Math Study Guide

Chapter 15 / Lesson 4
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