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

Answer:

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

$(b)\ y = 14.75$

Step-by-step 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)

$m =\frac{y_2 -y_1}{x_2 -x_1}$

$m =\frac{20-8}{8-24}$

$m =\frac{12}{-16}$

$m =-0.75$

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

$y = -0.75*15 + 26$

$y = -11.25 + 26$

$y = 14.75$