Esperanza worked 6 hours and earned $120. Today she worked 8 hours and earned $156 Write the equation that models the relationship between the number of hours worked and the amount of money she earns in y = mx + b
This can be written in the form of a linear equation as:
y = mx + b
where y is the amount of money earned, x is the number of hours worked, m is the rate of pay per hour, and b is the amount earned when no hours are worked (the y-intercept).
We can find m by calculating the rate of pay per hour. From the information given:
y = 120 when x = 6
and
y = 156 when x = 8
Using these values, we can find the slope (rate of pay per hour):
m = (y2 - y1) / (x2 - x1)
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18
Therefore, the equation that models the relationship between the number of hours worked and the amount of money earned is:
y = 18x + b
Now, we can use the first set of data to find the y-intercept, b. When x = 6 and y = 120:
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
Therefore, the complete equation is:
y = 18x + 12