Question

write the equation of the line, in standard form, that has an x-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 of the line , c is constant
The given line is 2x + y = -5 ⇒⇒⇒ ∴ y = -5 - 2x
The slope of the given line = -2
The required line is parallel to the given line . So, it have the same slope
∴ m = -2
∴ The general equation of the line will be ⇒⇒⇒ y = -2x + c
to find c we need a point on the line
x-intercept of 2 which mean the line pass through (2,0)

substitute with (2,0) to find C

∴ 0 = -2*2 +c ⇒⇒⇒ c = 4



The required line is ⇒⇒⇒⇒ y = -2x + 4

OR 2x + y = 4

Answer 2

Parallel to 2x+y=-5
2x+y-2x=-5-2x
y=-2x-5
y=mx+b
Slope: m=-2

As the line is parallel must have the same slope:
m=-2
And it has an x-intercept of 2: when x=2, y=0→Point: P1=(2,0)=(x1,y1)
x1=2, y1=0

y-y1=m(x-x1)
y-0=(-2)(x-2)
y=-2x+4
In standard form:
y+2x=-2x+2x+4
2x+y=4

Answer: The equation of the line, in standard form, that passes through the origin and is parallel to x+y=6 is x+y=0