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. Type your answer in the box provided to submit your solution.
To find the equation of the line that is parallel to x + y = 6 and passes through the origin, we need to find the slope of the given line and then use that to find the equation of the line passing through the origin.
The given line has the equation x + y = 6. To find its slope, we can rearrange it into slope-intercept form y = mx + b, where m is the slope. Subtracting x from both sides:
y = -x + 6
Now we can see that the slope of the given line is -1.
A line parallel to this line will have the same slope of -1.
The general equation of a line with a slope of m passing through the origin is y = mx.
So, the equation of the line passing through the origin and parallel to x + y = 6 is y = -x.
Therefore, the equation of the line in standard form is x + y = 0.