Question

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

⦁ How do you find rate of change using a graph?.
⦁ Simone claims the initial value and y-intercept are the same thing on a graph. Is she correct?
⦁ If you know that a line has a slope of 2 over 3 and a y-intercept of 7, what is the equation for that line in slope-intercept form?
⦁ Carson has $450 in his bank account and deposits $70 per month out of his babysitting money. Construct a linear function that models Carson’s bank balance for any given month.
⦁ What is the difference between a linear interval and a nonlinear interval on a graph? How would they look?

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) =
`(Change in y)/(Change in x)`

=
`( 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 =
`(Change in y(Rise))/(Change in x) (run)`

=
`(2)/(1)` = 2

3) slope =
`(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 =
`(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.