Question 30874: write an equation that represents the data in the table.
x|-2|0|2|4|6
y|9|5|1|-3|-7
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! x values increase by 2 every time. The y-values are decreasing by 4. So, as x increases, so the y-value "doubles". This is a "two-times table" just like 2,4,6,8,10, etc. Algebraically, this is y=2x.
Since we have "as x increase, so y decreases", then algebraically this is y=-2x.
Now we don't have THE 2-times table, we have a "shifted" version, so we need to find this shift value. To do this, put ANY value of x you have into our guess of y=-2x, get an answer then look at the actual answer and see what value we need to add or subtract to get that:
OK - i pick x=0, since this is the value of x to give me least work.
when x=0, y=-2x becomes y=0. However y should equal 5 when x=0, so we need to ADD 5 to our value of zero. So, the formula is now y=-2x+5.
Now, lets check it with another value of x. Pick one that is a fair way away from your original chosen value (x=0). I pick x=6
y=-2x+5
y=-2(6)+5
y = -12+5
y = -7 --> CORRECT
So, the equation of the line that has the set of coordinates on it is y=-2x+5
jon.
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