Question

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Answer 1

Answer:

The equation for the function g is g(x) = $\frac{12}{5}$ x - $\frac{29}{5}$ ⇒ C

Step-by-step explanation:

The form of the equation of the linear function is g(x) = m x + b, where

• m is the slope

• m is the y-intercept

The formula of the slope is m = $\frac{y2-y1}{x2-x1}$ , 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 = $\frac{-1--13}{2--3}$ = $\frac{-1+13}{2+3}$ = $\frac{12}{5}$

∴ m = $\frac{12}{5}$

→ Substitute in the form of the equation above

∴ g(x) = $\frac{12}{5}$ x + b

∵ There is only one choice that has m = $\frac{12}{5}$

∴ The equation for the function g is g(x) = $\frac{12}{5}$ x - $\frac{29}{5}$

∴ Choice C represents the equation of function g