How to Interpret Linear Equations

Linear equations help you interpret simple phenomena.
••• Digital Vision./Digital Vision/Getty Images

Simply put, a linear equation draws a straight line on a regular x-y graph. The equation holds two key pieces of information: the slope and the y-intercept. The slope’s sign tells you if the line rises or falls as you follow it left to right: A positive slope rises, and a negative one falls. The slope’s size governs how steeply it rises or falls. The intercept indicates where the line crosses the vertical y-axis. You’ll need beginning algebra skills to interpret linear equations.

Graphical Method

    Draw a vertical Y axis and horizontal X axis on the graph paper. The two lines should meet close to the center of the paper.

    Get the linear equation into the form Ax + By = C if it is not already in that form. For example, if you start with y = -2x + 3, add 2x to both sides of the equation to obtain 2x + y = 3.

    Set x = 0 and solve the equation for y. Using the example, y = 3.

    Set y = 0 and solve for x. From the example, 2x = 3, x = 3/2

    Plot the points you just obtained for x = 0 and y = 0. The example’s points are (0,3) and (3/2,0). Line the ruler up on the two points and connect them, passing the line through the x and y axis lines. For this line, note that it has a steep downward slope. It intercepts the y-axis at 3, so the has a positive beginning and proceeds downward.

Slope-Intercept Method

    Get the linear equation into the form y = Mx + B, where M equals the line's slope. For example, if you begin with 2y – 4x = 6, add 4x to both sides to obtain 2y = 4x + 6. Then divide through by 2 to get y = 2x + 3.

    Examine the equation’s slope, M, which is the number by x. In this example, M = 2. Because M is positive, the line will increase going left to right. If M were smaller than 1, the slope would be modest. Because the slope is 2, the slope is fairly steep.

    Examine the equation’s intercept, B. In this case, B = 3. If B = 0, the line passes through the origin, which is where the x and y coordinates meet. Because B = 3, you know that the line never passes through the origin; it has a positive beginning and steep upward slope, rising three units for every unit of horizontal length

    Things You'll Need

    • Graph paper
    • Straight edge or ruler
    • Calculator


    • Linear equations help you judge whether real-world tasks are successful. If the equation in the first example describes the results of your weight-loss regimen, you may be losing weight too rapidly, indicated by the steep downward slope. If the equation in the second example describes custom T-shirt sales, sales are increasing rapidly, and you may need to hire more help.

      A graphing calculator can rapidly draw graphs of linear equations, if you deal with them frequently.

Related Articles

How to Find Perpendicular Slope
How to Find a Parallel Line
How to Determine the Y-Intercept of a Trend Line
What is the Definition of Slope in Algebra?
How to Find Slope From an Equation
How to Solve for Slope in Algebra 1
Difference Between Parabola and Line Equation
What is Slope Intercept Form?
How to Find the Equation of a Scatter Plot
How to Find X-Intercept & Y-Intercept
How to Solve Slope-Intercept Form
How to Convert Slope Intercept Form to Standard Form
A Description of Parallel & Perpendicular Lines
How to Solve Hyperbolas
How to Convert an Equation Into Vertex Form
How to Graph Linear Equations With Two Variables
How to Tell If Lines Are Parallel, Perpendicular or...
How to Write a Linear Regression Equation
How to Calculate the Slope of Regression Line
How to Graph the Y-Intercept as a Fraction