Determine the slope and y-intercept of each function.

Question

(a)  Determine the slope and y-intercept of each function.
(b) Use the slope and y-intercept to graph the linear function.
(c) Determine the average rate of change of each function.
(d) Determine whether the linear function is increasing,decreasing,or constant

h(x) = -3x+4

Answer 1

Step 1:

The linear function is .

(a)

The function is .

Compare the function with slope - intercept form of line equation is .

Where, is the slope.

           is the - intercept.

Slope .

- intercept .

Step 2:

(b)

Graph the linear function using rise and run :

  - intercept is 4, so the line crosses the - axis at .

Using slope find the next point.

Slope = .

Start at point , move 3 units down and 1 unit right, then plot the point .

 Draw a line through these points.

 

Step 3:

Average rate of change of a linear function is .

Consider and .

The average rate of change .

Step 4:

The linear function is .

Slope is , which is negative.

So the function is decreasing on the interval .

Solution :

(a) Slope and - intercept .

(b) Graph of the function using slope and - intercept :

(c) The average rate of change is .

(d) The function is decreasing on the interval .