Question

⦁ How can a table be used to find the rate of change and the initial value? Describe the process.

Answer 1

1) Table can be used to find the rate of change and the initial value5

x ------> y

0 -------> 3

1 ------> 5

2 ------> 7

Rate of change (Slope) = $\frac{Change in y}{Change in x}$

=$\frac{ 7 - 5}{2 - 1}$

= 2/1 = 2

Rate of change = 2

Y intercept is the point where x=0

So y = 3 from the table.

2) Attached the graph of a line

Rate of change = $\frac{Change in y(Rise)}{Change in x} (run)$

= $\frac{2}{1}$ = 2

3) slope = $\frac{2}{3}$ and a y-intercept = 7

Equation of a line y= mx + b

Where m is the slope and b is the y intercept

Replace slope m and y intercept

m= 2/3, b= 7

Equation of a line : y = $\frac{2}{3}$ x + 7

4) Carson has $450 in his bank account and deposits $70 per month out of his babysitting money.

Initial amount in the bank (y intercept) b= $450

Deposited amount = 70 that is the slope m= 70

So the equation y = mx+ b , where x is the month

y = 70x + 450

Carson’s bank balance f(x) = 70x + 450

5) the graph of straight line is linear. In the graph x<1 that is (-infinity , 1) is linear.

The graph with curved line is non linear.In the graph x>1 that is (1, infinity ,) is non linear.

The graph is attached below.