Yesterday Esperanza worked for six hours and earned $120 today Esperanza worked eight hours and earned $156 write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns
Let the number of hours Esperanza works be represented by x, and the amount of money she earns be represented by y.
We can find the slope of the linear function by calculating the rate at which Esperanza earns money per hour.
The rate of change (slope) = (Change in y) / (Change in x)
From the given information:
When Esperanza worked for 6 hours, she earned $120.
When Esperanza worked for 8 hours, she earned $156.
Change in y = $156 - $120 = $36
Change in x = 8 - 6 = 2
Slope = (Change in y) / (Change in x) = $36 / 2 = $18 per hour
Using the point-slope form of a linear equation, which states that y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute the values:
x1 = 6, y1 = $120, and m = $18
y - $120 = $18(x - 6)
Simplifying the equation will provide the final answer:
y - $120 = $18x - $108
y = $18x + $12
Therefore, the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns is y = $18x + $12.