Write Slope-Intercept Form From a Table

Goal

Write an equation in slope-intercept form, (y=mx+b), using values from a table.

Method

1. Find the slope (m).

   • Choose two rows from the table: ((x_1,y_1)) and ((x_2,y_2)).
   • Compute [ m=\frac{y_2-y_1}{x_2-x_1}. ]
   • If the table shows a constant change in (y) for each change in (x), that pattern is the slope.

2. Find the y-intercept (b).

   • Use one point from the table and the slope in (y=mx+b).
   • Substitute the values and solve for (b).
   • If the table includes (x=0), then the matching (y)-value is the y-intercept directly.

3. Write the equation.

   • Put the slope and intercept into (y=mx+b).
   • Simplify carefully.

Check

Use another row from the table to test your equation. Substitute its (x)-value and see whether the output matches the table’s (y)-value. If it does, your equation is correct.

Tip

Watch signs carefully, especially if the values decrease or the intercept is negative.