The answers to the question on linear relationships are :
- [tex]y = \frac{5}{4}x + 10 [/tex]
The relationship between amount to be repaid, y and the amount borrowed, x :
X : ___$100__$200 __ $500 ___ $800
Y : ___$135__ $260 __ $635 ___ $1,010
General form of a linear equation :
- y = bx + c ; b = slope ; c = intercept
Slope, b = (y2 - y1) / (x2 - x1)
Slope, b = (1010 - 135) / (800 - 100) = 875/700 = [tex]\frac{5}{4} [/tex]
Intercept, c :
135 = 1.25(100) + c
135 - 125 = c
10 = c
Hence, the equation becomes ; [tex]y = \frac{5}{4}x + 10 [/tex]
2.) Amount earned, y by recycling x number of cans :
Amount paid per can = $0.05
Amount earned, y = 0.05x
Graph 1 :
y = 0.05x
x = 20
y = 0.05(20) = 1
Hence, $1 is earned for recycling 20 cans.
Hence, Graph A gives the correct representation of the scenario.
3.) Partial Representation
Partial representation are information display which only gives discrete values of X and Y values. Hence, Partial representation are : Table and Graph.
The equation given and verbal description gives a general form of both X and Y values covering all possible values of the variable.
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