Sets of points on a line are sometimes expressed in tables of x- and y-values. If you have a table of values for a linear equation, you can plot these ordered pairs to get an approximate sense of the line, including an estimate of its slope and intercepts. If you need more precise measurements, you can figure out the equation from a table of values by calculating the slope of the line and then using the point-slope formula.
Calculate the slope of the line by selecting any two points in your table. Subtract the second y-value from the first y-value. Then subtract the second x-value from the first x-value. Divide the difference in the y-values by the difference in the x-values to find the slope. For example, if your first point is (5,4) and your second point is (8,10), (10-4)/(8-5) simplifies to 6/3, which equals a slope of 2.
Substitute the slope and one ordered pair into the point-slope equation: y - y1 = m(x - x1). In the equation, m represents the slope. For example, using the slope 2 and the ordered pair (8,10), the equation is y - 10 = 2(x - 8). This simplifies to y = 2x - 6.
Check your work by putting one value from an ordered pair in your table into your final equation and solving. For example, if you put (5,4) into y = 2x - 6, you get 4 = 2(5) - 6, which is correct.
Tips & Warnings
- As long as you have two ordered pairs, you can find the slope and the equation.
- This strategy does not work for nonlinear equations, such as exponential equations, because they do not have a constant slope.
- "Algebra"; Michael Buckley; 2006
Definition of Table of Values
A table of values is a list of numbers that are used to substitute one variable, such as within an equation of...
How to Find Quadratic Equations From a Table
Given a quadratic equation, most algebra students could easily form a table of ordered pairs that describe the points on the parabola....
How to Identify Linear & Nonlinear Equations
Equations are mathematical statements, often using variables, that express the equality of two algebraic expressions. Linear statements look like lines when they...
How to Find Linear Equations
Linear equations form the basis of any Algebra I class, and students must understand them before they will be ready to move...
How to Do Function Tables in 6th Grade Math
Many students begin working with function tables -- also known as t-tables -- in sixth grade, as part of their preparation for...
How to Find the Slope of Linear Equations
Linear equations contain only linear terms. This means there are no square, cube or higher order terms in the equation. The slope...
How to Find Linear Equations From Tables
Sometimes you will be given a table of x-coordinates and y-coordinates and have to find the linear equation that fits that data....
How to Find an Ordered Pair From an Equation
Equations express relationships between variables and constants. The solutions to two-variable equations consist of two values, known as ordered pairs, and written...
How to Solve & Graph Quadratic Equations
Solving a quadratic equation typically involves factoring it as much as possible and determing the x intercepts and tip. One method of...
How to Find an Equation for a Linear Model
A linear model has a direct relationship between the two variables. For example, the annual earnings of a person working on a...
How to Find Linear Functions
At one time or another, you've probably used spreadsheet programs to find the best linear equation that fits a given set of...
How to Find a Rule and Equation of a Function
Starting with elementary school math and continuing through introductory algebra, students are sometimes asked to look at a table of a function's...