To find the slope of the line that passes through the points [tex]\((-4, 14)\)[/tex] and [tex]\((9, 7)\)[/tex], we can use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1) = (-4, 14)\)[/tex] and [tex]\((x_2, y_2) = (9, 7)\)[/tex].
First, we calculate the change in [tex]\(y\)[/tex] (also called the rise):
[tex]\[
\Delta y = y_2 - y_1 = 7 - 14 = -7
\][/tex]
Next, we calculate the change in [tex]\(x\)[/tex] (also called the run):
[tex]\[
\Delta x = x_2 - x_1 = 9 - (-4) = 9 + 4 = 13
\][/tex]
Using these values, we can now find the slope:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{-7}{13} \approx -0.5384615384615384
\][/tex]
Thus, the slope of the line that goes through the points [tex]\((-4, 14)\)[/tex] and [tex]\((9, 7)\)[/tex] is [tex]\(-0.5384615384615384\)[/tex].
