Answer
The function notation of the line through the points (4, 0) and (-4, -5) is:
$\\\\f(x)=\frac{5}{8}x -\frac{5}{2}$
Work Step by Step
RECALL:
$\\\\$ The function notation of a linear equation is $f(x)=mx+b$ where m = slope, b = y-intercept, and $f(x)$ is the y variable.
$\\\\\\$Solve for the slope using the slope formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ to have:
$\\\\\\m=\dfrac{-5-0}{-4-4}=\dfrac{-5}{-8}=\dfrac{5}{8}$
$\\\\\\$This means that the tentative equation is:
$\\\\f(x) = \frac{5}{8}x+b$
$\\\\\\$Solve for $b$ by substituting the coordinates of the point $(4, 0)$ into the tentative equation to have:
$\\\\f(4) = \frac{5}{8}(4) + b
\\\\0=\frac{20}{8}+b
\\\\0=\frac{5}{2}+b
\\\\-\frac{5}{2}=b$
