Respuesta :
Answer:
Value of y when x = [tex]1 \frac{1}{8}[/tex] 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 [tex]y = m \times x + c[/tex], where m is slope and c is constant.
Substituting values of [tex]y = 2 \frac{2}{3}[/tex] and [tex]x = \frac{1}{4}[/tex] in the assumed Equation:
[tex]y = m \times x + c[/tex]
[tex]2 \frac{2}{3} = m \times \frac{1}{4} + c[/tex]
[tex] \frac{8}{3} = m \times \frac{1}{4} + c[/tex]
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.
[tex] \frac{8}{3} = m \times \frac{1}{4}[/tex]
[tex]m = \frac{\frac{8}{3} }{\frac{1}{4} }[/tex]
[tex]m = \frac{8 \times 4}{3 \times 1}[/tex]
[tex]m =\frac{32}{3}[/tex]
Substituting value of m in the assumed equation,
[tex]y = \frac{32}{3} \times x[/tex]
Now when x = [tex]1 \frac{1}{8}[/tex] = [tex]\frac{9}{8}[/tex]
[tex]y = \frac{32 \times 9}{3 \times 8}[/tex]
[tex]y = 4 \times 3 = 12[/tex]
