how to write a slope int form with a table

Question

the table part a

time spent studying 10 20 30 40 50 write the slope intercept form of the equation for a line

score received 53 67 78 87 95 to fit for the data points (20,67) and (40,87)

part b

predict a students score if he spent 35 min studying

Answer 1

I think this question is asking you to fit a line for the points (20, 67) and (40, 87), come up with the equation for this line and then use the equation to predict the score when time spent is 35 minutes.

Independent variable = time studying = x

dependent variable = score received = y

Calculate slope = m = Δy/Δx = (y₂ -y₁)/(x₂ - x₁) = (87 - 67)/(40 - 20) = 20/20 = 1

slope intercept form y = mx + b

y = (1)x + b

plug in (40, 87) to solve for b

87 = 40 + b

47 = b

Equation is

y = x + 47

For 35 minutes studying:

y = 35 + 47 = 82 = score when studying 35 minutes