SOLUTION: The tables show linear relationships between x and y. Copy and complete the tables. x -2 0 ? 7 y -18 ? 12 27

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Question 936805: The tables show linear relationships between x and y. Copy and complete the tables.
x -2 0 ? 7
y -18 ? 12 27
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You have two known points and two unknown points. Find slope, pick one of the known points, form the point-slope form for the linear equation and simplify it.

SLOPE,
m=cross%28%2827-7%29%2F%28-18-%28-2%29%29%29-----This was my first mistake. Fixing the rest of the solution so it will be correct:

Fixing....
m=%2827-%28-18%29%29%2F%287-%28-2%29%29
m=45%2F9
m=5



Picking (27,7)
y-27=5%28x-7%29
y-27=5x-35
-5x%2By=27-35
5x-y=35-27
highlight%285x-y=8%29, standard form for the linear equation.

Now to finish your table:
-
x=0, what is y?
5x-8=y
5%2A0-8=y
y=-8 when x=0.
-
y=12, what is x?
5x-12=8
5x=8%2B12
5x=20
x=4 when y=12.



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
x|-2|+0| ? |+7
y|-18| ? |12|27
to find missing numbers in a table, we need find equation first
y=mx%2Bb where m is a slope and b is y-intercept

use two ordered pairs to find a slope: x%5B1%5D=-2,x%5B2%5D=7, y%5B1%5D=-18, and y%5B2%5D=27
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%2827-%28-18%29%29%2F%287-%28-2%29%29
m=%2827%2B18%29%2F%287%2B2%29
m=45%2F9
m=5
so far we have y=5x%2Bb

lets now use the Point-Slope formula to find the equation of the line
y-y%5B1%5D=5%28x-x%5B1%5D%29
plug in x%5B1%5D=-2 and y%5B1%5D=-18
y-%28-18%29=5%28x-%28-2%29%29
y%2B18=5%28x%2B2%29
y%2B18=5x%2B10
y=5x%2B10-18
y=5x-8
now we can complete the table:

x|-2|+0| 4 |+7
y|-18| +-8 |12|27
y=5%2A0-8=>y=-8
12=5x-8=>5x=20=>x=4

see the graph of this line and all points on it: