The table represents Monte's savings
The rate of change is 8. This means that he earns 8 dollars per hour
The graph represents Ramon's savings
The rate of change is 6. This means that he earns 6 dollars per hour
The answers to the questions are shown below
1) The rates of change represent the amount that each person earns per hour.
2) The rate of change of Monte's is greater. It means that he earns more per hour than Ramon.
3) We would find the equation in slope intercept form representing each person's savings. The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The y intercept is the value of y when x = 0. On the graph, it is the value of y at the point where the line cuts the vertical axis. We have
For the table,
when x = 0, y = 3
Thus, c = 3
m = 8
The equation for Monte's total savings is
y = 8x + 3
After 8 working hours, x = 8. We would substitute x = 8 into the equation. We have
y = 8 * 8 + 3 = 64 + 3
y = 67
Monte's total savings after 8 hours is $67
For the graph, c = 6
m = 6
The equation for Ramon's total savings is
y = 6x + 6
After 8 working hours, x = 8. We would substitute x = 8 into the equation. We have
y = 6 * 8 + 6 = 48 + 6
y = 54
Ramon's total savings after 8 hours is $54