Question

Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25

x y
1 5
2 20
3 45
4 80
5 125

x y
1 5
2 25
3 125
4 625
5 3125

x y
1 2
2 4
3 7
4 16
5 32​

Answer 1

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---$\frac{10-5}{2-1}$=5/1=5

x-values: 2, 3/y-values: 10, 15---$\frac{15-10}{3-2}$=5/1=5

x-values: 3, 4/y-vaues: 15, 20---$\frac{20-15}{4-3}$=5/1=5

x-values: 4, 5/y-values: 20, 25---$\frac{25-20}{5-4}$=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

Answer 2

The only table that represents a linear function is; Table 1

Linear function

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

• At x = 1, y = 5 and;

Slope = 5/1 = 5

• At x = 2; y = 10 and;

Slope = 10/2 = 5

• At x = 3, y = 15 and;

Slope = 15/3 = 5

• At x = 4, y = 20 and;

Slope = 20/4 = 5

• At x = 5, y = 25 and;

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

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