Question 1206810: the tables of ordered pairs represent some points on the graphs of two different lines.
Line a
X: -11, -6, -1, 4
Y: 81, 51, 21, -9
Line b
X: -9, -4, 1, 6
Y: 18, 3, -12, -27
Which systems of equations represents the graph of these two lines?
A) x - 6y = -90, x - 3y = 27
B) x + 6y = 90, x + 3y = -27
C) 6x - y = -15, 3x - y = -9
D) 6x + y = 15, 3x + y = -9
Found 3 solutions by MathLover1, josgarithmetic, greenestamps:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
Line 
 :  ,  , ,
 :  ,  ,  , 
use two points to find a slope
( ,) and ( ,)
substitute in equation above
 ...use one point to calculate 
so, equation of the line is
Line
: ,  ,  , 
:  ,  ,  ,
use two points to find a slope
(,) and (,)
 ...use one point to calculate
so, equation of the line is
answer:
D)  , 
Answer by josgarithmetic(39617)  (Show Source):
You can put this solution on YOUR website! You can use desmos.com, choose the Graphing Calculator tool, within that from the PLUS symbol at upper left, make a table for each of your sets of linear data points. Click the switch in each for "Line".
You can then read the slope and y intercept of each of the two lines and write in slope-intercept form. From those, change each equation into the Ax+By=C form; and make your answer selection.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
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.
Here is what I would do.
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.
That makes the equation of the form .
The answer choices all have the equations in Ax+By=C form; the equation of this line in that form is 
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.
 . Correct!
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.
 . Correct!
ANSWER: D
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