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

x+y=0

Step-by-step explanation:

Hi there!

We're given the line x+y=6 and we want to write the equation of the line that's parallel to x+y=6 and passes through the origin (or the point (0,0)) in standard form

Standard form is given as ax+by=c, where a, b, and c are free integer coefficients (the values of a, b, and c are numbers).

Note that a CANNOT be 0 and CANNOT be negative

First, let's find the slope of the line that will be parallel to x+y=6, as parallel lines have the same slope.

We'll do this by converting x+y=6 from standard form into slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

x+y=6

subtract x from both sides

y=-x+6

although there's no number in front of x, there's the negative sign, which means that the slope of x+y=6 is -1

Since parallel lines have the same slope, the slope of the new, parallel line is also -1

here's our equation so far in slope-intercept form:

y=-x+b

we need to find b

As the line will pass through (0,0), we can substitute it into the equation to solve for b

substitute 0 as x and 0 as y into the equation

0=-(0)+b

multiply

0=0+b

0=b

so the equation in slope-intercept form is y=-x+0

But remember! The problem asks for the answer in standard form

in that case, add x to both sides of the equation

x+y=0

Hope this helps!

step-by-step explanation: