Question

write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x+y=-5, include your work in your final answer.

Answer 1

The general equation of the line is  y = mx+c
Where m is the slope and c is a constant
the given line ⇒ 2x+y = -5 ⇒⇒ y = -2x -5
The slope of the given line = -2
The required line is parallel to the given line 
so the slope of the required line = -2 ⇒ ∴ y = -2x + c  →(1)

the required line has y-intercept of 2
So, the line is passing through ( 0 , 2) 
substitute in (1) to find c
∴ 2 = -2 * 0 + c  ⇒  c =2
∴ y = -2x + 2

The equation of the line, in standard form ⇒⇒  2x + y = 2