Question

X=3,5,6,9

Answer 1

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 $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ ,

where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ 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

∵ $(x_{1},y_{1})$ = (3 , 2)

∵ $(x_{2},y_{2})$ = (5 , 6)

- Use the formula of the slope to find m

∵ $m=\frac{6-2}{5-3}=\frac{4}{2}$

∴ 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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