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

To solve this problem you must apply the proccedure shown below:
You have that the line is parallel to x+y=6, this means that both lines have the same slope. You can calculate the slope as below:
y=mx+b
m is the slope and b is the y-intercept

x+y=6
y=-x+6
The slope is m=-1

As the line passes through the origin, b=0, therefore, you have:
y=-x+0
y=-x
x+y=0

The answer is: x+y=0