How to Work Out a Gradient of a Curve

Curve plotted on graph paper
••• graph image by Roman Sigaev from

In mathematics, a line graph is used to represent the values of a function. Functions of x that do not contain exponents (such as x=y or y=2x+1) are linear in nature, so the gradient (rise over run) is simple to calculate.

Functions of x that contain exponents (such as y=2x^2 +1) are more difficult to calculate, since the y-component of the line may curve in relation to the x-axis.

    Calculate the corresponding "Y-axis" values of ten "X-axis" numbers. For example, if y=x^2, calculate the Y-axis values for X where X equals -5, -4, -3, -2, -1, 0, 1, 2, 3 and 4. Plot these values on the graphing paper, where the X value is the horizontal axis, and the Y value is the vertical axis.

    Choose two ascending points on the graph (such as "X=2" and "X=3"). Draw a straight line from one point to the other.

    Count the number of lines on the vertical axis between the two points, and write this number down as the numerator. Count the number of lines on the horizontal axis between the two points, and write this number down as the denominator. The gradient is the numerator divided by the denominator.

    Things You'll Need

    • Mathematical function of X (such as "y=x^2")
    • Scientific calculator
    • Graph paper
    • Pen or pencil
    • Protractor


    • Since a slope of a curve is constantly changing, the gradient will vary between any two points. As such, a any gradient measurement must be performed at one point or between a set of two points, as opposed to along the whole curve.

Related Articles

How to Find Equations of Tangent Lines
How to Find the X Intercept of a Function
How to Find the Angle of a Curve
How to Calculate the Slope of Regression Line
How to Figure Out the Slope of a Line
How to Divide Rational Numbers
How to Find the Slope of a Plotted Line With the TI-84...
How to Graph the Y-Intercept as a Fraction
How to Calculate the Midpoint Between Two Numbers
How to Graph and Find the Solution on a Calculator
How to Find the Slope of a Nonlinear Line
How to Find a Tangent Line to a Curve
How to Find a Z Score
How to Create Linear Equations
How to Graph Parabolas on a TI-84 Calculator
How to Find the Vertices of an Ellipse
How to Determine the Y-Intercept of a Trend Line
How Do You Simplify Your Slope
How to Straighten an Inverse Curve
How to Convert Graphs to Equations