Question

14) Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

Nishant

Answer 1

Your Answer:-

We are given that y is directly proportional to x

So,

$\tt y \propto x$

In the first case

We have,

And we have y = 12 and x = 4

$\tt y \propto x \\\\ \tt Removing \ \ proportional \ \ symbol \ \ by \ \ a \ \ constant\\\\ Let \ \ the \ \ constant \ \ be \ \ 'p' \\\\ y = px \\\\ \Rightarrow 12 = 4p\\\\ \Rightarrow 3=p$

We have the value of p as 3

$\tt y = px \\\\ Replacing \ \ the \ \ values \ \ of \ \ x \ \ and \ \ p \\\\ \tt \Rightarrow y = 3(5) \\\\ \tt \Rightarrow y=15$

So, the value of y = 15 when x = 5

2nd Method:

$\tt \dfrac{12}{4}=\dfrac{y}{5} \\\\ \tt \Rightarrow 3 = \dfrac{y}{5} \\\\ \tt \Rightarrow 3 \times 5 = y \\\\ \tt \Rightarrow15 =y$