Question

What is the rule/output?

Answer 1

The rule is y = 4x - 5.

Explanation:

Notice that if we start with x = 1 and increase x by 1, we get 2. Simultaneously, y starts with -1 and becomes 3. Thus, the slope is m = rise / run = 4/1, or 4.

The rule is y = 4x - 5.

Check: Suppose we pick input 4 from the table. Does this rule produce output 11? Is 11 = 4(4) - 5 true? YES.

Answer 2

y = 4x - 5

Explanation:

Have you been taught to set up 2 equations and 2 unknowns?

That is actually the only way I could do this.

y = mx + b

x = 2

y = 3

3 = 2m + b

x = 1

y = -1

-1 = m + b Multiply by 2. That means that the m term will cancel.

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-2 =2m +2b

3 = 2m + b Subtract

-5 = b

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3 = 2m + b Substitute - 5 for b

3 = 2m - 5 Add 5 to both sides.

3+5= 2m-5+5 Combine

8 = 2m Divide by 2

8/2=2m/2

m = 4