Question

find the inverse function in slope - intercept form (mx + b):
$f(x)=-\frac{5}{2}x + 5$

Explanation:

Step1: Replace $f(x)$ with $y$

$y = -\frac{5}{2}x + 5$

Step2: Swap $x$ and $y$

$x = -\frac{5}{2}y + 5$

Step3: Isolate the term with $y$

$x - 5 = -\frac{5}{2}y$

Step4: Solve for $y$

$y = -\frac{2}{5}(x - 5)$
$y = -\frac{2}{5}x + 2$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = -\frac{2}{5}x + 2$

Answer:

$f^{-1}(x) = -\frac{2}{5}x + 2$