From the graph we have the following:
Week number Number of hours worked
1 5 hours
2 10 hours
3 15 hours
4 20 hours
Here, the number of hours vary directly with the number of weeks.
To find the constant of proportionality we have:
Where week number is x and number of hours is y, constant of proprtionality = k
y = kx
5 = 1k
Constant of proportionality, k = 5
To find the slope, we have:
The slope of the line is 5.
To find the number of hours the volunteer will work in 16 weeks we have:
y = 5 x 16
y = 80 hours
The volunteer will work for 80 hours in 16 weeks.
The equation to describe the relationship is:
Use the slope intercept form: y = mx + b
Where m = slope and b = y-intercept
Here y-intercept = 0, and slope = 5
The equation is:
y = 5x + 0
y = 5x
ANSWER:
Constant of proportionality = 5
Slope = 5
The volunteer will work for 80 hours in 16 weeks
Equation: y = 5x