Answer: y = (1/3)x - 5
This is the same as writing
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Step-by-step explanation:
Assume we have a linear pattern matching the form y = mx+b.
The first row has x = 12 lead to y = -1
The second row has x = 3 lead to y = -4
This produces the two points (12,-1) and (3,-4)
Let's find the slope through those points.
m = (y2-y1)/(x2-x1)
m = (-4-(-1))/(3-12)
m = (-4+1)/(3-12)
m = -3/(-9)
m = 1/3
The slope is 1/3.
The y intercept is b = -5 since x = 0 leads to y = -5
We go from y = mx+b to y = (1/3)x - 5
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To verify we have the correct equation, plug in each left side value as x values.
Let's try x = 12
y = (1/3)x - 5
y = (1/3)*12 - 5
y = 4 - 5
y = -1
This shows that the input x = 12 maps to the output y = -1
i.e. 12 ↦ −1 is the case here.
Repeat for x = 3
y = (1/3)x - 5
y = (1/3)*3 - 5
y = 1 - 5
y = -4
We can see that 3 ↦ −4 occurs.
I'll let you check the others, but you should find that the other mappings hold true as well. Therefore, the answer has been fully confirmed.