Question

A

Answer 1

To start, the equation has to be converted to slope-intercept form, or $y=mx+b$. Start by subtracting x from both sides; $x-x+2y=4$, $2y=4-x$. Switch 4 and -x around to conform to the formula; $2y=-x+4$. Then divide by 2 to isolate y; $y=-\frac{1}{2}x+2$. 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 $-\frac{1}{4}$, the opposite reciprocal of $-\frac{1}{5}$ is 5) the opposite reciprocal of $-\frac{1}{2}$  is 2. So the equation of the line is $y=2x$, and the answer is A.

Answer 2

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 = - $\frac{1}{2}$ x + 2 ← in slope- intercept form

with slope m = - $\frac{1}{2}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{1}{2} }$ = 2