Question

find the linear function with the following properties.
$f(-5) = 5$
$f(-7) = 2$
$f(x) = $

Explanation:

Step1: Calculate slope $m$

$m = \frac{f(-5)-f(-7)}{-5-(-7)} = \frac{5-2}{-5+7} = \frac{3}{2}$

Step2: Use point-slope form

Use point $(-5, 5)$: $y - 5 = \frac{3}{2}(x + 5)$

Step3: Simplify to slope-intercept

$y = \frac{3}{2}x + \frac{15}{2} + 5 = \frac{3}{2}x + \frac{15}{2} + \frac{10}{2} = \frac{3}{2}x + \frac{25}{2}$

Answer:

$\frac{3}{2}x + \frac{25}{2}$