Answer-
The equation that describes the pattern is,
[tex]\boxed{\boxed{y=2{x}+30}}[/tex]
Solution-
P = Number of minutes Rodney spends practicing playing the piano
G = Number of minutes Rodney spends practicing playing the guitar
Taking P on x axis and G on y axis, the points are,
[tex](0,30),(15,60),(30,90),(45,120)[/tex]
Taking first two points i.e [tex](0,30),(15,60)[/tex], the line equation will be,
[tex]\Rightarrow \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}[/tex]
[tex]\Rightarrow \dfrac{y-30}{60-30}=\dfrac{x-0}{15-0}[/tex]
[tex]\Rightarrow \dfrac{y-30}{30}=\dfrac{x}{15}[/tex]
[tex]\Rightarrow 15(y-30)=30{x}[/tex]
[tex]\Rightarrow y-30=2{x}[/tex]
[tex]\Rightarrow y=2{x}+30[/tex]
Putting the other two points i.e [tex](30,90),(45,120)[/tex] in the equation, they also satisfy the equation. That means they are also on the same line [tex]y=2{x}+30[/tex].
From the result, it is evident that P and G are linearly related.
