Final answer:
To determine the equation representing the linear relationship between hours worked and money earned for a welder, we calculate the slope as $19/hour using the two given points. Then, with the point-slope form, we find the y-intercept to be $18, resulting in the linear equation y = $19x + $18.
Step-by-step explanation:
The student is looking to find an equation that represents a linear relationship between the number of hours a welder works and the money earned. Since we know the welder earns $113 in 5 hours working at a new job and $75 in 3 hours of working, we can use these two points to determine the slope (rate of change) and y-intercept of the linear equation.
First, let's calculate the slope (m) which is the change in money earned per hour of work:
Slope = (change in money earned) / (change in hours worked)
m = ($113 - $75) / (5 hours - 3 hours)
m = $38 / 2 hours
= $19/hour
So, the welder earns $19 for each hour of work. Given the slope and one of the points, say (5, $113), we can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
y - $113 = $19(x - 5)
Now to find the y-intercept (b), we can simplify the equation:
y = $19x - $95 + $113
y = $19x + $18
Thus, the equation y = mx + b that represents the relationship between hours worked (x) and money earned (y) is:
y = $19x + $18