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Maths-

SAT

Easy

Question

The scatterplot above shows the maximum height h, in feet (ft), and maximum speed s, in miles per hour (mph), of 12 roller coasters as well as the line of best fit for the data. Of the following, which best represents an equation for the line of best fit?

s = 0.21h + 32
s = 0.43h + 32
s = 0.21h + 62
s = 0.43h + 62

The correct answer is: s = 0.21h + 32

The line passes thorough (180, 70) & (320, 100)
The line is $fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction equals fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction$
$fraction numerator y minus 70 over denominator 100 minus 70 end fraction equals fraction numerator x minus 180 over denominator 320 minus 180 end fraction$
$fraction numerator y minus 70 over denominator 30 end fraction equals fraction numerator x minus 180 over denominator 140 end fraction$
14(y - 70) = 3(x - 180)
14y - 980 = 3x - 540
Here x = h & y = s
14s - 980 = 3h - 540
14s = 3h - 540 + 980 = 3h + 440
$s equals fraction numerator 3 h over denominator 14 end fraction plus 440 over 14$
s = 0.21h + 31.4

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