Yesterday Henry worked 6 hours and earned $120 Today he worked 8 hours and earned $158 Write the equation that models the relationship between the number of hours he worked and the amount of money he earns
Let x represent the number of hours worked and y represent the amount of money earned.
The equation can be written as y = mx + b, where m is the rate of pay per hour and b is the amount earned when no hours are worked.
From the information given:
When x = 6, y = $120
When x = 8, y = $158
Using these points, we can calculate the rate of pay per hour (m) by finding the slope of the line:
m = (y2 - y1) / (x2 - x1)
m = ($158 - $120) / (8 - 6)
m = $38 / 2
m = $19
Now we can find the amount earned when no hours are worked (b) by substituting the values of one of the points into the equation:
$120 = $19(6) + b
$120 = $114 + b
b = $120 - $114
b = $6
Therefore, the equation that models the relationship between the number of hours worked and the amount of money earned is:
y = 19x + 6.