So there are a couple of ways to do this. One would be to try and fit all of these equations into the same form (such as y=mx + b) and see which of the answer options match the original one. Personally, though, I think the easiest way is to consider the fact that any two distinct points in the same plane will determine a line.
This means if any answer option contains both points that are given [(-7, 11) and (8, -9)], then that answer option represents the same line as is represented by the equation in the question.
So for answer option 1:
y = (-4/3) * x + (5/3) : If we plug in (-7, 11), we get (-4/3) * (-7) + 5/3 = 28/3 + 5/3 =33/3 = 11. Thus, our first answer option contains the point (-7,11). Next, we check to see if it contains (8, -9). If we plug in (8, -9), we get: (-4/3) * 8 + 5/3 = -32/3 + 5/3 = -27/3 = -9. Thus, our first answer option also contains the point (8, -9). Since two points determine a line and our answer option contains both points, we thus know that our first answer option represents the same line as the one in the question.
We can then repeat this process for each of the other options.
An example of an equation that doesn’t represent the line in the question can be seen with answer option 2:
3y = -4x + 40. If we plug in (-7, 11), we get 3(11)= -4 (-7) + 40 -> 33 = (28) + 40 -> 33 = 68. Since this obviously isn’t true, this means that answer option 2 does not contain the point (-7, 11) and thus does not represent the same line as the one in the question. (If you graph this line out, you’ll actually see that it’s parallel to the line in the question but with a y-intercept that is much higher)!
(x + 7) Distribute
YES, these match.
