Create an equation that matches this table

The equation that matches the given table is

y = 10x + 40

Solution:

General equation of a line : y = mx + c

Let us find the equation of the table.

Common differences of X:

0 – 1 = 1, 1 – 2 = 1, 3 – 2 = 1, 4 – 3 = 1, 5 – 4 = 1

Common differences of Y:

50 – 40 = 10, 60 – 50 = 10, 70 – 60 = 10, 80 – 70 = 10, 90 – 80 = 10

m = 10

Substitute m = 10 in general equation of a line

y = 10x + c

To find the constant term, substitute x = 0 and y = 40.

40 = 10(0) + c

40 = 0 + c

40 = c

c = 40

Therefore the equation of a line is y = 10x + 40.

Hence the equation that matches the given table is y = 10x + 40.

That is the third choice.

If we add the 2 equations we get

2y = -12 so y = -6

substituting in one of the equations we get x = 0