Question

If y= 2 2/3 when x= 1/4, find y when x= 1 1/8

Answer 1

Answer:

Value of y when x = $1 \frac{1}{8}$ is y = 12

Explanation:

In order to find different values of y for different values of x, we need to develop equation of y in terms of x.

Let us assume $y = m \times x + c$, where m is slope and c is constant.

Substituting values of $y = 2 \frac{2}{3}$ and $x = \frac{1}{4}$ in the assumed Equation:

$y = m \times x + c$

$2 \frac{2}{3} = m \times \frac{1}{4} + c$

$\frac{8}{3} = m \times \frac{1}{4} + c$

In order to equate the equation, c needs to be zero, because for any other value of c except zero, the equation would not equate.

$\frac{8}{3} = m \times \frac{1}{4}$

$m = \frac{\frac{8}{3} }{\frac{1}{4} }$

$m = \frac{8 \times 4}{3 \times 1}$

$m =\frac{32}{3}$

Substituting value of m in the assumed equation,

$y = \frac{32}{3} \times x$

Now when x = $1 \frac{1}{8}$ = $\frac{9}{8}$

$y = \frac{32 \times 9}{3 \times 8}$

$y = 4 \times 3 = 12$