Find the equation of the line: parallel to 3x−y=11 through (−2, 0).

I believe it is:

slope-intercept form: y=3x+6

standard form: -3x+y=6 or 3x-y=-6

point slope-form: y-0=3(x+2)

Step-by-step explanation:

First, I put 3x-y=11 into slope-intercept form:

Subtract 3x from both sides: 3x-3x-y=11-3x

That becomes -y=-3x+11

Divide both sides by -1: -y/-1=(-3x+11)/-1

That becomes y=3x-11\

Then, the definition of a parallel line is having the same slope but different y-intercepts, so I dropped the -11 as the y-intercept, and I rewrote the equation as y=3x+b, where b is the y-intercept.

Now, I have to find the y-intercept of the parallel line, so I plug the coordinates (-2,0) into the equation for x and y to solve for the y-intercept

Write the equation out with what you have so far: y=3x+b

Substitute the coordinates (-2,0) in for x and y: 0=3(-2)+b

That becomes 0=-6+b

Add 6 to both sides: 0+6=-6+6+b

That becomes 6=b, which means that 6 is your y-intercept.

Finally, you have gathered everything you need to write the parallel line in equation format.

The parallel line's equation is

in slope-intercept form: y=3x+6

in standard form: -3x+y=6 or 3x-y=-6

in point-slope form: y-0=3(x+2)