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 or use the upload option to submit your solution.
clearly, if the line contains (0,0),
x+y=0
Can someone explain how he got to this conclusion? I understand he answer and everything, but if you had to show work what would you do?
Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
(1, 5) and (-2, 3)
To find the equation of the line that is parallel to x + y = 6 and passes through the origin, we need to determine the slope of the given line.
The equation x + y = 6 can be rewritten in slope-intercept form (y = mx + b) by subtracting x from both sides:
y = -x + 6
Comparing this equation with y = mx + b, we can see that the slope (m) of the given line is -1.
Since parallel lines have the same slope, the slope of the line we are looking for is also -1.
The equation of a line with slope -1 passing through the origin (0,0) can be written as:
y = -x
However, the equation is usually stated in standard form, which can be achieved by moving all the terms to the left side of the equation. So let's rewrite it in standard form:
x + y = 0
Therefore, the equation of the line, in standard form, that passes through the origin and is parallel to x + y = 6 is x + y = 0.