Skill: Determine slope from a table

Slope tells how much $y$ changes for each change in $x$. For a table, use two corresponding ordered pairs and calculate

$$m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}.$$

Always subtract in the same order: if you use the second $y$ minus the first $y$, also use the second $x$ minus the first $x$.

Suppose the table shows:

$x$	$y$
$1$	$5$
$3$	$9$
$6$	$15$

Step 1: Choose two points.
Use $(1,5)$ and $(6,15)$. The $x$-values do not need to be next to each other in the table.

Step 2: Find the change in $y$.

$$\Delta y=15-5=10$$

Step 3: Find the change in $x$.

$$\Delta x=6-1=5$$

Step 4: Divide the change in $y$ by the change in $x$.

$$m=\frac{\Delta y}{\Delta x}=\frac{10}{5}=2$$

The slope is $\boxed{2}$. This means that for every increase of $1$ in $x$, $y$ increases by $2$.

Do not calculate $\frac{y}{x}$; slope is the ratio of the changes, $\frac{\Delta y}{\Delta x}$. Since the table represents a linear relationship, any two points should give the same slope.