Question

For 3 hours of work, a consultant charges $300. For 5 hours of work, she charges $400. How do you write an equation to represent this?

Answer 1

`y=50x+150`

Explanation:

This linear equation is represented by a straight line where the input is x for the number of hours worked, and the output is y for the income earned. Given here are two points on the line so the slope of the line can be calculated as follow:
`x_1=3,y_1=300` and `x_2=5,y_2=400` => find the slope m:
`m=(y_2-y_1)/(x_2-x_1)`
`m=(400-300)/(5-3)=100/2=50`
`y-y_1=m(x-x_1)` =>equation of the line in point-slope form:
in this case:
`y-300=50(x-3)`
`y=50x+150` => equation of the line in slope intercept form