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To start, the equation has to be converted to slope-intercept form, or [tex]y=mx+b[/tex]. Start by subtracting x from both sides; [tex]x-x+2y=4[/tex], [tex]2y=4-x[/tex]. Switch 4 and -x around to conform to the formula; [tex]2y=-x+4[/tex]. Then divide by 2 to isolate y; [tex]y=-\frac{1}{2}x+2 [/tex]. This is the final equation. Because the slope of a line perpendicular is always the opposite reciprocal (i.e. The opposite reciprocal of 4 is [tex]-\frac{1}{4} [/tex], the opposite reciprocal of [tex]-\frac{1}{5} [/tex] is 5) the opposite reciprocal of [tex]-\frac{1}{2} [/tex]  is 2. So the equation of the line is [tex]y=2x[/tex], and the answer is A.

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x + 2y = 4 ( subtract x from both sides )

2y = - x + 4 ( divide terms by 2 )

y = - [tex]\frac{1}{2} [/tex] x + 2 ← in slope- intercept form

with slope m = - [tex]\frac{1}{2} [/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular} [/tex] = - [tex]\frac{1}{m} [/tex] = - [tex]\frac{1}{-\frac{1}{2} } [/tex] = 2

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