Question

which linear function represents the line given by the point-slope equation $y + 7 = -\frac{2}{3}(x + 6)$?○ $f(x) = -\frac{2}{3}x - 11$○ $f(x) = -\frac{2}{3}x - 1$○ $f(x) = -\frac{2}{3}x + 3$○ $f(x) = -\frac{2}{3}x + 13$

Explanation:

Step1: Expand the right-hand side

$y + 7 = -\frac{2}{3}x - \frac{2}{3} \times 6$
$y + 7 = -\frac{2}{3}x - 4$

Step2: Isolate y by subtracting 7

$y = -\frac{2}{3}x - 4 - 7$
$y = -\frac{2}{3}x - 11$

Answer:

$\boldsymbol{f(x) = -\frac{2}{3}x - 11}$ (Option 1)