which linear function represents the line given by the point-slope equation $y + 7 = -\frac{2}{3}(x +…

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

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

Answer

Answer:

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

Explanation:

Step1: Distribute the slope term

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

Step2: Isolate $y$

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

Step3: Rewrite as function

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