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Ira Lisetskai [31]
2 years ago
5

2.3.2: Michael Myers predicts that SAT scores predict college graduation rates in a linear fashion. U of M has an average SAT of

1450 and a graduation rate of 90%. GVSU has an average SAT of 1110 and a graduation rate of 69.6%. Write an equation to represent the linear relationship . Be sure your equation is in slope-intercept form
Mathematics
1 answer:
AleksAgata [21]2 years ago
3 0

Answer:

y = \frac{5000r}{3} -50

Step-by-step explanation:

Represent the SAT score with y and the rate with r.

So, we have:

(r_1,y_1) = (90\%,1450)

(r_2,y_2) = (69.6\%,1110)

Required

Determine the equation in slope intercept form

First, we calculate the slope

m =\frac{y_2 - y_1}{r_2 - r_1}

This gives:

m =\frac{1110 - 1450}{69.6\% - 90\%}

m =\frac{-340}{-20.4\%}

Convert percentage to decimal

m =\frac{-340}{-0.204}

m =\frac{340}{0.204}

Multiply by 1000/1000

m =\frac{340*1000}{0.204*1000}

m =\frac{340000}{204}

m = \frac{5000}{3}

The equation is then calculated as:

y - y_1 = m(r - r_1)

This gives:

y - 1450 = \frac{5000}{3}(r - 90\%)

Open Bracket

y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*90\%

Convert percentage to decimal

y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*0.90

y - 1450 = \frac{5000r}{3} - 5000*0.30

y - 1450 = \frac{5000r}{3} - 1500

Make y the subject

y = \frac{5000r}{3} - 1500+1450

y = \frac{5000r}{3} -50

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