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The linear equation that describes the data is f(x) = 2x - 4
Step-by-step explanation:
The form of the linear equation is y = mx + b, where
- m is the slope of the line which represents the equation
- b is the y-intercept (y at x = 0)
The formula of the slope is ,
where and
are 2 points on the line
The table:
→ x : 3 , 5 , 6 , 9
→ f(x) : 2 , 6 , 8 , 14
To find the equation use any two points from the table above
∵ f(x) = y
∵ = (3 , 2)
∵ = (5 , 6)
- Use the formula of the slope to find m
∵
∴ m = 2
Substitute the value of m in the form of the equation below
∵ y = mx + b
∴ y = 2x + b
To find b substitute x and y in the equation by the coordinates of any point from the table above
∵ x = 6 and y = 8
∴ 8 = 2(6) + b
∴ 8 = 12 + b
- Subtract 12 from both sides
∴ -4 = b
- Substitute the value of b in the equation
∴ y = 2x + (-4)
∴ y = 2x - 4
∴ f(x) = 2x - 4
The linear equation that describes the data is f(x) = 2x - 4
Learn more:
You can learn more about the linear equation in brainly.com/question/9801816
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