Question

Find the slope of the line through the given points.(-4,7) and (-1,-3)Is the slope increasing or decreasing?

Answer 1

• The following formula can be used to find the slope of a line:

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

These points are on the line:

$(x_1,y_1);(x_2,y_2)$

Given the following points:

$\mleft(-4,7\mright);(-1,-3)$

Then, you can set up that:

$\begin{gathered} y_2=-3_{} \\ y_1=7 \\ x_2=-1 \\ x_1=-4 \end{gathered}$

Therefore, substituting values into the formula and evaluating, you get:

$\begin{gathered} m=\frac{-3-7}{-1-(-4)} \\ \\ m=\frac{-10}{-1+4} \\ \\ m=-\frac{10}{3} \end{gathered}$

• As you can notice, the slope is negative. Therefore, you can determine that it is decreasing.

Therefore, the answers are:

• Slope of the line:

$m=-\frac{10}{3}$

• It is decreasing.