Answer:
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)
, which is option D.