The linear function is .

(a)

The function is .

Compare the function with slope - intercept form of line equation ,

where is the slope and is the - intercept.

Slope of line equation is .

- intercept of line equation is .

(b)

Graph :

Graph the linear function using rise and run method.

- intercept is , hence the line crosses the - axis at .

Slope = .

Start at point , move unit up and units right, then plot the point .

Draw a line through these points.

(c)

Average rate of change of a linear function is .

Consider and .

The average rate of change .

The average rate of change is .

(d)

The linear function is .

Slope is , which is positive.

So the function is increasing on the interval .

(a) Slope and - intercept .

(b) Graph of the function :

(c) The average rate of change is .

(d) The function is increasing.