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Rod is paid an overtime rate of $25 per hour after he earns his basic wage of $600 per week. Write an equation in slope-intercept form for the total pay p if he works h hours of overtime.
The monthly cost C of Marge’s phone plan is given by C = 40 + m, where m is the number of extra minutes she uses in that month. Name the slope and y-intercept in this situation and explain what each represent.
Solution
1.) Rod is paid an overtime rate of $25 per hour after he earns his basic wage of $600 per week. Write an equation in slope-intercept form for the total pay p if he works h hours of overtime.
Slope-intercept form: y=ax+b
- the total pay p is our y; p=y
- h (number of hours overtime) is our x; h=x
- overtime rate of $25 per hour means that every hour (h) he gets $25 so we have 25 for the “a” or slope in the slope-intercept form; a=25
- basic wage of $600 per week means that that is a constant, and it’s fixed, it doesn’t change, so in the slope-intercept equation that is going to be “b”; b=600
- plug it in and get: p= 25h + 600
2.) The monthly cost C of Marge’s phone plan is given by C = 40 + m, where m is the number of extra minutes she uses in that month. Name the slope and y-intercept in this situation and explain what each represent.
C = 40 + m
If it’s not clear to you immediately, rewrite it like this:
C= 1m+ 40
And then compare it to slope-intercept form y=ax+b
That means that:
C=y
m=x
40=b which is y-intercept
a=1 which is the slope
So, slope is 1, and y-intercept is 40.