Chapter 9, Problem 4STP

To determine

To calculate:To find slopeof the line that passes through $R\left(4,1\right)$ and $S\left(-2,6\right)$ .

Answer to Problem 4STP

The slopeof the line that passes through $R\left(4,1\right)$ and $S\left(-2,6\right)$ is $-\frac{5}{6}$

Explanation of Solution

Given information:

Points - $R\left(4,1\right)$ and $S\left(-2,6\right)$

Formula Used:

The slope-intercept form of the equation of a line is $y=mx+b$ , where $m$ is the slope of the line, and $b$ is the y-intercept.

In case of two points given $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ , slope is given by

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

GivenPoints - $R\left(4,1\right)$ and $S\left(-2,6\right)$

Using the above explanation, we have slope of the line as −

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values, we have:

  $m=\frac{6-1}{-2-4}$

Solving the above equation, we have:

  $m=-\frac{5}{6}$

The slope is $-\frac{5}{6}$

Conclusion:

The slope of the line that passes through $R\left(4,1\right)$ and $S\left(-2,6\right)$ is $-\frac{5}{6}$