Question

hari's weekly allowance varies depending on the number of chores he does he received $14 in allowance the week he did 12 chores, and $12 in allowance the week he did 8 chores. write an equation for his allowance in slope intercept form.

Answer 1

y=(1/2)x+8

Step-by-step explanation:

When Hari does 12 chores, his allowance is $14.

• We write this as coordinate (12, 14).

When Hari does 8 chores, his allowance is $12.

• We write this as coordinate (8, 12).

To write the equation for his allowance in slope-intercept form, we begin by solving for the slope.

`\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =(14-12)/(12-8) \\ =(2)/(4) \\ m=(1)/(2) \end{gathered}`

Next, we substitute the slope and any of the points (I use (8, 12)) into the point-slope form.

`y-y_1=m(x-x_1)`
`\begin{gathered} y-12=(1)/(2)(x-8) \\ y=(1)/(2)x-(8)/(2)+12 \\ y=(1)/(2)x-4+12 \\ y=(1)/(2)x+8 \end{gathered}`

The equation for his allowance in slope-intercept form is:

`y=(1)/(2)x+8`