Question

The scatter plot shows the time spent watching TV, x, and the time spent doing homework, y, by each of 23 students last week.

Answer 1

`(a)\ y = -0.75x + 26`

`(b)\ y = 14.75`

Explanation:

Given

See attachment for scatter plot

Required

Equation of the line of best fit

Pick any two points on the line

`(x_1,y_1) = (24,8)`

`(x_2,y_2) = (8,20)`

Calculate the slope (m)

`m =(y_2 -y_1)/(x_2 -x_1)`

`m =(20-8)/(8-24)`

`m =(12)/(-16)`

`m =-0.75`

The equation is then calculated using:

`y = m(x - x_1) + y_1`

So, we have:

`y = -0.75(x - 24) + 8`

`y = -0.75x + 18 + 8`

`y = -0.75x + 26`

Solving (b): y, when
`x = 15`

`y = -0.75x + 26` becomes

`y = -0.75*15 + 26`

`y = -11.25 + 26`

`y = 14.75`