Question

how does the slope of g(x) compare to the slope of f(x)?
the slope of g(x) is the opposite of the slope of f(x)
the slope of g(x) is less than the slope of f(x).
the slope of g(x) is greater than the slope of f(x)
the slope of g(x) is equal to the slope of f(x).

Explanation:

Step1: Find slope of \( g(x) \)

Points on \( g(x) \): \((-5, 0)\) and \((0, 2)\).
Slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
\( m_{g} = \frac{2 - 0}{0 - (-5)} = \frac{2}{5} = 0.4 \).

Step2: Find slope of \( f(x) \)

Points on \( f(x) \): \((0, -2)\) and \((2, 3)\).
\( m_{f} = \frac{3 - (-2)}{2 - 0} = \frac{5}{2} = 2.5 \).

Step3: Compare slopes

\( 0.4 < 2.5 \), so slope of \( g(x) \) is less than slope of \( f(x) \).

Answer:

The slope of \( g(x) \) is less than the slope of \( f(x) \) (the corresponding option, e.g., if it's the second option: "The slope of \( g(x) \) is less than the slope of \( f(x) \)").