Answer:
(c) [tex]x + 2y = 8[/tex]
Step-by-step explanation:
The question is missing some important data which is necessary to solve it.
The correct question is as follows:
Which equation shows [tex]y=-\frac{1}{2}x+4[/tex] is in standard form?
(a) [tex]2x-y=8[/tex]
(b) [tex]x + 2y=-8[/tex]
(c) [tex]x + 2y = 8[/tex]
(d) [tex]2x + y = 8[/tex]
Solution:
Given equation:
[tex]y=-\frac{1}{2}x+4[/tex]
To convert the given equation to standard form.
The standard form of a linear equation is given by:
[tex]Ax+By=c[/tex]
where
A is a positive integer and B and C are integers
We have:
[tex]y=-\frac{1}{2}x+4[/tex]
Multiply both sides by 2 to remove the fraction
[tex]2y=(-\frac{1}{2}x\times 2)+(4\times 2)[/tex]
[tex]2y=-x+8[/tex]
Adding [tex]x[/tex] both sides
[tex]x+2y=x-x+8[/tex]
[tex]x+2y=8[/tex]
∴ The standard form of the equation is ⇒ [tex]x+2y=8[/tex]
