Question

Find the Pattern

12 ↦ −1
3 ↦ −4
0 ↦ −5
−1 ↦ −5.3…
−9 ↦ −8

I have to find a formula to get from the left number to the right number, but I cannot find the pattern. How do I do this, and what is the solution?

Answer 1

Answer: y = (1/3)x - 5

This is the same as writing
`y = (1)/(3)x-5`

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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.