Question

Write an equation for the table 2 5 5.6 14 7 17.5 8 20

Answer 1

The equation for the table is y = 2.5 x

Step-by-step explanation:

The table is:

• x  →  2    :    5.6    :    7    :    8
• y  →  5    :    14      :  17.5  :    20

Lets check if the table represents the linear relation by find the ratio between the change of each two consecutive y-coordinates and the change of their corresponding x-coordinates

∵ $\frac{14-5}{5.6-2}=\frac{9}{3.6}=2.5$

∵ $\frac{17.5-14}{7-5.6}=\frac{3.5}{1.4}=2.5$

∵ $\frac{20-17.5}{8-7}=\frac{2.5}{1}=2.5$

∴ The rate of change between each two points is constant

∴ The table represent a linear equation

The form of linear equation is y = m x + b, where m is the rate of change and b is value y when x = 0

∵ m = 2.5

- Substitute it in the form of the equation

∴ y = 2.5 x + b

- To find b substitute x and y by the coordinates of any point

  in the table above

∵ x = 2 and y = 5

∴ 5 = 2.5(2) + b

∴ 5 = 5 + b

- Subtract 5 from both sides

∴ 0 = b

∴ y = 2.5 x

The equation for the table is y = 2.5 x

Learn more:

You can learn more about the linear equations in brainly.com/question/4326955

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