Answer:
[tex]y = \frac{5000r}{3} -50[/tex]
Step-by-step explanation:
Represent the SAT score with y and the rate with r.
So, we have:
[tex](r_1,y_1) = (90\%,1450)[/tex]
[tex](r_2,y_2) = (69.6\%,1110)[/tex]
Required
Determine the equation in slope intercept form
First, we calculate the slope
[tex]m =\frac{y_2 - y_1}{r_2 - r_1}[/tex]
This gives:
[tex]m =\frac{1110 - 1450}{69.6\% - 90\%}[/tex]
[tex]m =\frac{-340}{-20.4\%}[/tex]
Convert percentage to decimal
[tex]m =\frac{-340}{-0.204}[/tex]
[tex]m =\frac{340}{0.204}[/tex]
Multiply by 1000/1000
[tex]m =\frac{340*1000}{0.204*1000}[/tex]
[tex]m =\frac{340000}{204}[/tex]
[tex]m = \frac{5000}{3}[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(r - r_1)[/tex]
This gives:
[tex]y - 1450 = \frac{5000}{3}(r - 90\%)[/tex]
Open Bracket
[tex]y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*90\%[/tex]
Convert percentage to decimal
[tex]y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*0.90[/tex]
[tex]y - 1450 = \frac{5000r}{3} - 5000*0.30[/tex]
[tex]y - 1450 = \frac{5000r}{3} - 1500[/tex]
Make y the subject
[tex]y = \frac{5000r}{3} - 1500+1450[/tex]
[tex]y = \frac{5000r}{3} -50[/tex]
