Question

study time in X hours
8
5
7
12
10

test grade Y in percent
68
50
62
92
80
a)model the date in a linear function
b)interpret the meaning of the slope

Answer 1

5 , 50

7 , 62

8 , 68

10 , 80

12 , 92


Different :

7 - 5 = 2

62 - 50 = 12

12 / 2 = 6

That mean :

y increases for 6 when x increases for 1

That is slope.


Slope intercept equation of straight line :

y = m ( x + x1 ) + y1


In this case :

m = ( y2 - y1 ) / ( x2 - x1 )

You can take any two points , example:

x1 = 8

y1 = 68

x2 = 10

y2 = 80


m = ( y2 - y1 ) / ( x2 - x1 )

m = ( 80 - 68 ) / ( 10 - 8 ) = 12 / 2 = 6

Slope = 6


y = m ( x - x1 ) + y1

y = 6 ( x - 8 ) + 68

y = 6 x - 48 + 68

y = 6 x + 20


Proof :

x = 8

y = 6 * 8 + 20 = 48 + 2 = 68


x = 5

y = 6 * 5 + 20 = 30 + 20 = 50


x = 7

y = 6 * 7 + 20 = 42 + 20 = 62


x = 12

y = 6 * 12 + 20 = 72 + 20 = 92


x = 10

y = 6 * 10 + 20 = 60 + 20 = 80

Answer 2

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