The equation for the table is y = 2.5 x
Step-by-step explanation:
The table is:
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
∵ [tex]\frac{14-5}{5.6-2}=\frac{9}{3.6}=2.5[/tex]
∵ [tex]\frac{17.5-14}{7-5.6}=\frac{3.5}{1.4}=2.5[/tex]
∵ [tex]\frac{20-17.5}{8-7}=\frac{2.5}{1}=2.5[/tex]
∴ 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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