Question

Hari's weekly allowance varies depending on the number of chores he does. He received $16 in allowance the week he did 8 chores, and $14 in allowance the week he did 4 chores. Write an equation for his allowance in slope-intercept form.

Answer 1

`y=(1)/(2)x+12`

Explanation:

The problem is point to a linear relation where we have two given points

`(4,14)(8,16)`

The chores represent the independent variable, and the money represents the dependent variable, because they amount of money depends on the number of chores Hari did.

Using these two points, we first find the slope:

`m=(y_(2)-y_(1))/(x_(2)-x_(1) )=(16-14)/(8-4)=(2)/(4)=(1)/(2)`

Now, we use the slope, one point and the point-slope formula:

`y-y_(1)=m(x-x_(1))\\y-14=(1)/(2)(x-4)\\ y=(1)/(2)x-2+14\\ y=(1)/(2)x+12`

Therefore, the slope-intercept form is

`y=(1)/(2)x+12`