Question 1206810
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Instead of doing all the formal algebra to find the equation of each line, let's work this problem as if we are working on a timed test, where the speed of getting the answer is important, so we want to get the answer doing as little work as possible.<br>
Here is what I would do.<br>
For the first line, the x values are -9,-4, 1, 6, a constant difference of 5; the y values are 81, 51, 21,-9, a constant difference of -30.  So the slope of the line (change in y divided by change in x) is -30/5 = -6.<br>
That makes the equation of the form {{{y=-6x+b}}}.<br>
The answer choices all have the equations in Ax+By=C form; the equation of this line in that form is {{{6x+y=b}}}<br>
Only one of the answer choices (D) is in that form.  Using any one of the four given points for this line, see if that equation is correct.<br>
{{{6x+y=6(-11)+81=-66+81=15}}}. Correct!<br>
So answer choice D has the right equation for the first line; since it is the only possible correct answer, use any one of the points for line 2 to verify that the equation for line 2 in answer choice D is correct.<br>
{{{3x+y=3(-9)+18=-27+18=-9}}}. Correct!<br>
ANSWER: D<br>