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
The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] ,
where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] 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
∵ [tex](x_{1},y_{1})[/tex] = (3 , 2)
∵ [tex](x_{2},y_{2})[/tex] = (5 , 6)
- Use the formula of the slope to find m
∵ [tex]m=\frac{6-2}{5-3}=\frac{4}{2}[/tex]
∴ 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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