Answer:
First option: [tex]f(x)=-\frac{2}{3}x-11[/tex]
Step-by-step explanation:
Given the point-slope equation [tex]y+7=-\frac{2}{3}(x+6)[/tex], you need to solve for [tex]y[/tex], because you are looking for the equation of the line in slope-intercept form:
[tex]y=mx+b[/tex]
Being [tex]m[/tex] the slope of that line, and [tex]b[/tex] the intersection of the line with the y-axis.
Then:
Apply Distributive property:
[tex]y+7=-\frac{2}{3}x-4[/tex]
Subtract 7 from both sides:
[tex]y+7-(7)=-\frac{2}{3}x-4-(7)\\y=-\frac{2}{3}x-11[/tex]
Rewrite the equation:
[tex]f(x)=-\frac{2}{3}x-11[/tex] (The linear function of the First option)
