Question

Which equation gives the rule for this table?

Answer 1

Answer: $y=x-3$

Step-by-step 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  $m=\frac{y_2-y_1}{x_2-x_1}$:

$m=\frac{5-2}{8-5}=\frac{3}{3}=1$

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:

$y=x-3$