Question

function 2 is defined by line g.

Explanation:

Step1: Identify two points on line \( g \)

From the graph, line \( g \) passes through \( (0, 2) \) (y-intercept) and \( (4, 0) \) (x-intercept).

Step2: Calculate the slope \( m \)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using \( (x_1, y_1) = (0, 2) \) and \( (x_2, y_2) = (4, 0) \):
\( m = \frac{0 - 2}{4 - 0} = \frac{-2}{4} = -\frac{1}{2} \)

Step3: Write the equation in slope - intercept form \( y = mx + b \)

We know \( m = -\frac{1}{2} \) and \( b = 2 \) (from the y - intercept \( (0, 2) \)). So the equation of line \( g \) is \( y = -\frac{1}{2}x + 2 \)

(If the question was to find the equation of the line, this is the result. If other aspects like rate of change etc., the slope \( -\frac{1}{2} \) is the rate of change)

Answer:

If finding the equation: \( y = -\frac{1}{2}x + 2 \); If finding the slope: \( -\frac{1}{2} \) (depending on the actual question, but based on the graph analysis above)