Question

write the equation of the line in standard form that passes through the origin and is parallel to x + y equals 6​

Answer 1

y+x = 0

Explanation:

We have given an equation.

x+y = 6

We have to find the equation of the line in standard form that passes through the origin.

Ax+By = C is standard form of equation of line.

y= mx+c is slope-intercept form of equation where m is slope and c isy-intercept.

given equation in slope-intercept form is:

y = -x+6

hence, m = -1 and c = 6

Parallel equations have same slopes.

Hence, m = -1

Line passes through the origin. Hence, c = 0

Putting in slope-intercept form, we have

y = (-1)x+(0)

y = -x+0

y = -x

y+x = 0 is standard form of equation of line that passes through the origin and parallel to x+y= 6.

Answer 2

Answer:
`x+y=0`

Explanation:

The equation of the line slope-intercept form is:

`y=mx+b`

Where m is the slope and b is the y-interecept.

The standard form is:

`Ax+By=C`

You know that must be parallel to
`x+y=6`, therefore both have the same slope. So you must solve for y:

`y=-x+6`

Substitute the slope m=-1. Since the line passes through the origin b=0:

`y=-x`

Then in standar form is:

`x+y=0`