Answer:
The equation for the function g is g(x) = [tex]\frac{12}{5}[/tex] x - [tex]\frac{29}{5}[/tex] ⇒ C
Step-by-step explanation:
The form of the equation of the linear function is g(x) = m x + b, where
The formula of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are 2 points on the line represents the function
From the given table
∵ The points (-3, -13) and (2, -1) belong to the function g(x)
∴ x1 = -3 and y1 = -13
∴ x2 = 2 and y2 = -1
→ Substitute them in the formula above to find m
∵ m = [tex]\frac{-1--13}{2--3}[/tex] = [tex]\frac{-1+13}{2+3}[/tex] = [tex]\frac{12}{5}[/tex]
∴ m = [tex]\frac{12}{5}[/tex]
→ Substitute in the form of the equation above
∴ g(x) = [tex]\frac{12}{5}[/tex] x + b
∵ There is only one choice that has m = [tex]\frac{12}{5}[/tex]
∴ The equation for the function g is g(x) = [tex]\frac{12}{5}[/tex] x - [tex]\frac{29}{5}[/tex]
∴ Choice C represents the equation of function g
