Slope From a Table

Slope from a Table

When a table gives pairs of values, the slope tells how much the output changes for each 1-unit change in the input. In algebra, slope is often written as

[ m=\frac{\Delta y}{\Delta x} ]

where (\Delta y) is the change in the vertical values and (\Delta x) is the change in the horizontal values.

1) Pick two rows

Choose any two points from the table, written as ((x_1,y_1)) and ((x_2,y_2)).

2) Find the change in y and x

Subtract the y-values: (y_2-y_1).
Subtract the x-values: (x_2-x_1).

3) Form the slope and simplify

Substitute into

[ m=\frac{y_2-y_1}{x_2-x_1} ]

Then reduce the fraction if possible. A negative slope means the output decreases as the input increases.

4) Check your work

Use a second pair of rows, if possible. The slope should match every time for a linear table. If the values do not give the same result, recheck your subtraction and sign.

Quick tip

If the x-values increase by a constant amount, look at how the y-values change over the same steps. That ratio is the slope.