Answered

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

Sagot :

MrRoyal

Answer:

[tex](a)\ y = -0.75x + 26[/tex]

[tex](b)\ y = 14.75[/tex]

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

[tex](x_1,y_1) = (24,8)[/tex]

[tex](x_2,y_2) = (8,20)[/tex]

Calculate the slope (m)

[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]

[tex]m =\frac{20-8}{8-24}[/tex]

[tex]m =\frac{12}{-16}[/tex]

[tex]m =-0.75[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = -0.75(x - 24) + 8[/tex]

[tex]y = -0.75x + 18 + 8[/tex]

[tex]y = -0.75x + 26[/tex]

Solving (b): y, when [tex]x = 15[/tex]

[tex]y = -0.75x + 26[/tex] becomes

[tex]y = -0.75*15 + 26[/tex]

[tex]y = -11.25 + 26[/tex]

[tex]y = 14.75[/tex]

View image MrRoyal
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