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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3 years ago