Question

Which equation gives the rule for this table?

Answer 1

Answer:
`y=x-3`

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

The first step is to choose two points from the table. These can be;

(5,2) and (8,5).

You can say that:

`y_2=5\\y_1=2\\\\x_2=8\\x_1=5`

Now you must substitute values into the formula
`m=(y_2-y_1)/(x_2-x_1)`:

`m=(5-2)/(8-5)=(3)/(3)=1`

Substitute the slope and the coordinates of any point from the table into
`y=mx+b` and solve for "b":

`2=(1)(5)+b\\\\2-5=b\\\\b=-3`

Therefore, the equation that gives the rule for the table is:

`y=x-3`