Question

1 c Find the constant of proportionality for the table of values. 3 4 5 y 3 6 7.5 The constant of proportionality is k =

Answer 1

Let:

`\begin{gathered} k=\text{constant of proportionality:} \\ y=kx \\ for\colon \\ x=2 \\ y=3 \\ so\colon \\ 3=2k \\ \text{solve for k:} \\ k=(3)/(2)=1.5 \end{gathered}`

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Let:

x = Number of hours

Let:

`\begin{gathered} (x1,y1)=(4,58) \\ (x2,y2)=(6,87) \\ k=(y2-y1)/(x2-x1)=(87-58)/(6-4)=(29)/(2)=14.5 \\ y-y1=m(x-x1) \\ y-58=(29)/(2)(x-4) \\ y-58=(29)/(2)x-58 \\ y=(29)/(2)x \end{gathered}`