Graph PlottersPlot a linear graph, explore a linear graph equation, and see its slope, intercepts, and direction update instantly.
Hover to inspect coordinates. Drag the graph to pan the view or use the wheel and zoom controls to explore the function.
ABOUT THE TOOL
A linear function has the form y = mx + b. Its graph is a straight line with slope m and y-intercept b.
HOW TO USE IT
A linear graph shows a constant rate of change. In y = mx + b, m is the slope and b is the y-intercept. The slope tells you how far the line moves vertically for each one-unit move to the right, while the intercept shows where the line crosses the y-axis.
Use this linear graph calculator to see the slope, y-intercept, x-intercept, and direction of a line. When m is not zero, the x-intercept is −b/m. A positive slope rises from left to right, a negative slope falls, and a zero slope creates a horizontal line.
Enter any finite values for m and b, or type a complete equation such as y = 2x − 5. Change one value at a time to connect the algebraic form with the line on the graph. Use zoom controls and the coordinate cursor to inspect the line at any x-value.
A linear graph has a constant first difference: equal changes in x produce equal changes in y. In slope-intercept form y = mx + b, m is the rate of change and b is the value when x = 0. Point-slope form y − y₁ = m(x − x₁) is useful when a point and slope are known, while standard form can make intercepts easier to compare. All non-vertical linear graphs appear as straight lines.
For y = 2x − 4, the slope is 2, the y-intercept is (0, −4), and the x-intercept is (2, 0). Plot the line, check those two intercepts, and use the cursor to verify that moving one unit right raises y by two units. If m changes to −2, the same intercept pattern becomes a falling line. This rise-and-run check is the quickest way to validate a linear graph.
Suppose x increases from 1 to 4 while y increases from 5 to 14. The slope is (14 − 5)/(4 − 1) = 3, so the rate of change is constant at 3. Using y = 3x + 2 gives both points and predicts the y-intercept (0, 2). Enter the equation, inspect the intercepts, and use the rise-and-run pattern to confirm that the line is linear.
Use slope-intercept form y = mx + b when you know slope and y-intercept. Use point-slope form y − y₁ = m(x − x₁) when you know one point and the slope. Convert to standard form when comparing intercepts or working with integer coefficients. The graph is the same after equivalent algebraic forms are simplified, so the calculator can be used as a visual check on each form.
Explore related tools as you study functions: start with the online graphing calculator to plot a general equation, then use the linear graph calculator for constant rates and the slope calculator for rise over run. When a curve meets the x-axis, check the x intercept calculator; for parabolas, compare the quadratic graph calculator and vertex calculator. Use the cubic graph calculator for polynomial end behavior, the sine graph calculator and cosine graph calculator for periodic models, and the phase shift calculator for horizontal movement. The function transformations calculator compares parent and transformed curves, while the absolute value graph calculator explains V-shaped graphs. For growth and inverse relationships, try the exponential growth graph calculator, reciprocal graph calculator, and log graph calculator. For asymptote and periodic-function practice, use the tangent graph calculator, secant graph calculator, and cosecant graph calculator to compare branches, gaps, and repeating behavior.
COMMON QUESTIONS
m is the slope. It measures the change in y for every one-unit change in x.
b is the y-intercept, the value of y when x equals zero.
Set y to zero and solve 0 = mx + b, giving x = −b/m when m is not zero.
A linear graph is a straight line and has a constant slope. Equal changes in x produce equal changes in y.
No. A vertical line has undefined slope and is written as x = c instead.
Plot the y-intercept, use the slope as rise over run to find another point, and draw the straight line through them. The calculator provides a visual check.