Find an equation of the line passing through the given points. Use function notation to write the equation.
1 answer:
Step-by-step explanation:
First, find the slope of the line using the slope formula where (1, -3) = (x1, y1) and (3, 7) = (x2, y2).
![m = \frac{y2 - y1}{x2 - x1}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20)
![m = \frac{7 - ( - 3)}{3 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B7%20-%20%28%20-%203%29%7D%7B3%20-%201%7D%20)
![m = \frac{10}{2} = 5](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B10%7D%7B2%7D%20%20%3D%205)
Use point-slope form to find the equation.
![y - y1 = m(x - x1)](https://tex.z-dn.net/?f=y%20-%20y1%20%3D%20m%28x%20-%20x1%29)
![y - ( - 3) = 5(x - 1)](https://tex.z-dn.net/?f=y%20-%20%28%20-%203%29%20%3D%205%28x%20-%201%29)
![y + 3 = 5x - 5](https://tex.z-dn.net/?f=y%20%2B%203%20%3D%205x%20-%205)
Subtract 3 on both sides
![y = 5x - 8](https://tex.z-dn.net/?f=y%20%3D%205x%20-%208)
To put the equation in function notation, simply change the y to f(x) and you'll get
f(x) = 5x - 8
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