Answer:
The table represents a linear function because the rate of change is constant or all the points lie on a straight line.
Step-by-step explanation:
From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).
The slope of the line is
m= y2-y1/x2-x1 = 10-5/4-2 = 5/2
The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.
From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.
Since the rate of change (slope) is same for all points, therefore the table represents a linear function.
If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a linear function.
The data given in the table represents the function is linear function.
Input(x) = -2 -5 -8 -11
Output (y) = 7 4 1 -2
Functions is defined as relationship between sets of values.
Here,
The data available in the table, input and output.
In input(x) there is difference of -3 in consecutive values, and in output(y) values there is difference of -3 in consecutive values so difference is same in both values.
Thus, the relationship shows in the table is linear. So as the function is linear.
learn more about function here:
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