How to Convert Graphs to Equations

Steeper graphs have equations with larger gradients.
••• Jupiterimages/Goodshoot/Getty Images

A straight graph visually depicts a mathematical function. The x- and y-coordinates of the graph's points represent two sets of quantities and the graph plots the relationship between the two. The equation of the line is the algebraic function that derives the y-values from the x-coordinates. The two factors that define this equation are the line's gradient, which is its slope, and its y-intercept, which is y's value when x is 0.

    Identify the coordinates of the intersection between the graph and the y-axis. For this example, imagine an intersection at the point (0, 8).

    Identify one other point on the graph. For this example, imagine that another point on the graph has the coordinates (3, 2).

    Subtract the first point's y-coordinate from the second's -- 8 - 2 = 6.

    Subtract the first point's x-coordinate from the second's -- 0 - 3 = -3.

    Divide the difference in y-coordinates by the difference in x-coordinates -- 6 ÷ -3 = -2. This is the line's gradient.

    Insert the line's gradient and the y-coordinate from Step 1 as "m" and "c" in the equation "y = mx + c." With this example, that gives -- y = -2x + 8. That's the equation of the graph.

Related Articles

How to Create Linear Equations
How to Calculate the Slope of a Line of Best Fit
How to Find the Slope & the Equation of the Tangent...
How to Find The Slope of a Line Given Two Points
How to Determine the Y-Intercept of a Trend Line
How to Find Quadratic Equations From a Table
How to Graph and Find the Solution on a Calculator
How to Find the Slope of a Nonlinear Line
How to Find the Angle of a Curve
How to Solve a Parabola
How to Find X-Intercept & Y-Intercept
How to Find the Slope in a Circle
How to Figure Out the Slope of a Line
How to Write a Linear Regression Equation
How to Find Equations of Tangent Lines
How to Write Quadratic Equations Given a Vertex & Point
How to Calculate Angles Between Two Lines
How to Solve for Slope in Algebra 1
How to Find an Equation Given a Table of Numbers
How to Solve Slope-Intercept Form