Q3. - Algebra 2

Question

3. What is the slope of the line that contains the points $\left(15,7\right)\text{ and }\left(6,4\right)$?

$\text{A}.\frac{1}{4}\text{ B. }\frac{1}{3}\text{ C.}\frac{3}{8}\text{ D.}\frac{2}{3}$

Step-by-Step Solution

Answer

The slope of a line that contains the points $\left(15,7\right)\text{ and }\left(6,4\right)$ is $\frac{1}{3}$.

Step-1 – Apply the concept of slope

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

Symbolically, the slope m of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$ where $x_1\ne x_2$.

Step-2 – Example of a slope through two points

Suppose a line passes through the points $(2,4),(3,0)$. Then the slope of the line passing through these points is given by 

$\begin{array}{c}m=\frac{0-4}{3-2}\\ =\frac{-4}{1}\\ =-4\end{array}$

Step-3 – Calculate the slope of the given points

The given points are $\left(15,7\right)\text{ and }(6,4)$. Therefore, $x_1=15;x_2=6;y_1=7;y_2=4$.

Hence the slope of the line through these points is calculated as 

$\begin{array}{c}m=\frac{4-7}{6-15}\\ =\frac{-3}{-9}\\ =\frac{1}{3}\end{array}$

Hence the slope is $\frac{1}{3}$.

Therefore, option B is correct.