Question

 Find the linear function y, where y depends on t, the number of years since 1980. Helppp due Sunday

Answer 1

Answer: -2t + 220

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Step-by-step explanation:

For now I'll use x in place of t.

Two points on that line segment are: (15,190) and (25,170)

Use the slope formula to get the following

`(x_1,y_1) = (15,190) \text{ and } (x_2,y_2) = (25,170)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (170 - 190)/(25 - 15)\\\\m = (-20)/(10)\\\\m = -2\\\\`

The slope is -2.

A slope of -2 means we go down 2 each time we move to the right 1.

In short: "down 2, right 1".

Now use point-slope form to determine the equation

`y - y_1 = m(x - x_1)\\\\y - 190 = -2(x - 15)\\\\y - 190 = -2x + 30\\\\y = -2x + 30 + 190\\\\y = -2x + 220\\\\`

The last step to do is replace x with t and we get y = -2t+220 which is the final answer.

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Check:

Plugging in t = 15 should lead to y = 190.

y = -2t + 220

y = -2(15) + 220

y = -30 + 220

y = 190

So far so good.

Now we need to check if t = 25 leads to y = 170.

y = -2t + 220

y = -2(25) + 220

y = -50 + 220

y = 170

That works as well.

We have confirmed the points (15,190) and (25,170) are on this equation. The answer is confirmed.