Question

The table shows the relationship between the number of minutes Rodney spends practicing playing the piano p, and the number of minutes he spends playing his guitar g. Write an equation that describes the pattern in the table
G 30 60 90 120
P 0 15 30 45

Answer 1

Answer-

The equation that describes the pattern is,

$\boxed{\boxed{y=2{x}+30}}$

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,

$(0,30),(15,60),(30,90),(45,120)$

Taking first two points i.e $(0,30),(15,60)$, the line equation will be,

$\Rightarrow \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}$

$\Rightarrow \dfrac{y-30}{60-30}=\dfrac{x-0}{15-0}$

$\Rightarrow \dfrac{y-30}{30}=\dfrac{x}{15}$

$\Rightarrow 15(y-30)=30{x}$

$\Rightarrow y-30=2{x}$

$\Rightarrow y=2{x}+30$

Putting the other two points i.e $(30,90),(45,120)$ in the equation, they also satisfy the equation. That means they are also on the same line $y=2{x}+30$.

From the result, it is evident that P and G are linearly related.