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Delicious77 [7]
3 years ago
15

Let f be a linear function such that f(1) = 5 and f(3) = 9. Find an equation for f(x).

Mathematics
1 answer:
sleet_krkn [62]3 years ago
4 0

Answer:

f(x)=2x+3

Step-by-step explanation:

So we know that:

f(1)=5 \text{ and } f(3)=9

In other words, we have 2 coordinates: (1,5) and (3,9).

With this, we can figure out the slope. Let (1,5) be x₁ and y₁ and let (3,9) be x₂ and y₂. The slope formula is:

m=\frac{y_2-y_1}{x_2-x_1}

Substitute:

m=\frac{9-5}{3-1}\\m=4/2=2

So, the slope is 2.

Now, use the point-slope form to figure out the y-intercept. The point-slope form is:

y-y_1=m(x-x_1)

For consistency, let's continue to use (1,5) as x₁ and y₁. Now, we can use 2 as m. Thus:

y-(5)=2(x-1)

Distribute:

y-5=2x-2

Add 5 to both sides:

y=2x+3

So:

f(x)=2x+3

And that's our equation :)

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