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. Type your answer in the box provided or use the upload option to submit your solution.

Answer 1

Answer:

$x+y=0$

Step-by-step explanation:

We are asked to write an equation of the line, in standard form, that passes through the origin and is parallel to $x+y=6$.

First of all, we will convert our given equation in the slope-intercept form of equation $y=mx+b$, where,

m = Slope of line,

b = The y-intercept.

First of all, we will subtract x from from both sides of our given equation as:

$x-x+y=6-x$

$y=-x+6$

We can see that slope of our given line is $-1$ and y-intercept is 6.

We know that parallel lines have same slope and different y-intercepts.

Since we need to find the equation of line that passes through origin, so we will substitute $m=-1$ and coordinates of origin (0,0) in slope-intercept form of equation.

$0=-1*0+b$

$0=0+b$

$0=b$

The equation of a line parallel line to our given line and passes through origin would be $y=-x+0$

Now, we will add x on both sides of our equation.

$y+x=-x+x+0$

$x+y=0$

Therefore, our required equation would be $x+y=0$.

Answer 2

Y = - x + 6
m = - 1

0 = - 1 ( 0 ) + c
c = 0
y = - x

x + y = 0