Question

write the equation of the line, in standard form, that passes through the origin and is parallel to x+y=6. 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
given x+y = 6 ⇒⇒⇒ y = -x + 6
The slope of the given line = -1
The required line is parallel to the given line .
So, the slope of the required line = -1
∴ m = -1
The general equation will be ⇒⇒⇒ y = -x + c
The origin (0,0) point is on the required line
substitutes to find C
∴ 0 = 0 + c ⇒⇒⇒ c = 0
The equation of required line is ⇒⇒⇒ y = -x OR y + x = 0

Answer 2

Parallel to x+y=6
x+y-x=6-x
y=-x+6
y=mx+b
Slope: m=-1

As the line is parallel must have the same slope:
m=-1
And it passes through the origin, then b=0
y=mx+b
y=(-1)x+0
y=-x
In standard form:
y+x=-x+x
x+y=0

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