(A)
The equation is 3x + 7y =8 can be simplified as,
[tex]\begin{gathered} 3x+7y=8 \\ 7y=8-3x \\ y=-\frac{3}{7}x+\frac{8}{7} \end{gathered}[/tex]
The value of y (output) is unique for every different x (input) values. So equation is function.
(B)
The general expression for the linear equation is,
[tex]y=mx+c[/tex]
Where m is slope and b is y intercept.
So equation 3x + 7y =8 is linear equation with slope of -3/7 and y intercept of 8/7.
(C)
The equation is linear equation, so option C is incorrect.
(D)
The equation for the proportional relation is,
[tex]y=kx[/tex]
But the equation is simplified as,
[tex]y=-\frac{3}{7}x+\frac{8}{7}[/tex]
Thus equation in not a proportional. Option D is incorrect.
(E)
Substitute 0 for x in equation 3x + 7y =8 to obtain the value of y.
[tex]\begin{gathered} 3\cdot0+7y=8 \\ y=\frac{8}{7} \end{gathered}[/tex]
Option E is correct.
(F)
Substitute 2 for y in the equation 3x + 7y =8 to obtain the value of x.
[tex]\begin{gathered} 3x+7\cdot2=8 \\ 3x=8-14 \\ x=-\frac{6}{3} \\ =-2 \end{gathered}[/tex]
The value of x is -2 and not possible to obtain x = 2. So option F is incorrect.
Correct answer are:
A. function
B. linear
