Graph PlottersEnter two coordinates to calculate slope, point-slope equation, angle of inclination, distance, and the working steps.
y = 2x
Drag the graph to pan the view or use the wheel and zoom controls to explore the line.
ABOUT THE TOOL
Slope is the rate of change between two points. A line with slope 2 rises 2 units for every 1 unit moved to the right, while a vertical line has an undefined slope because its run is zero.
HOW TO USE IT
Slope measures how steep a line is: how much y changes for each unit of x. Given two points, use m = (y₂ − y₁)/(x₂ − x₁). The numerator is the rise and the denominator is the run. A positive slope rises from left to right, a negative slope falls, and a zero slope is horizontal.
Enter the coordinates of P₁ and P₂, subtract the y-values to find the rise, subtract the x-values to find the run, and divide. The calculator also gives the line equation, angle of inclination, distance, and a graph through the selected points.
When the two x-coordinates are equal, the run is zero and the line is vertical, so its slope is undefined. A horizontal line has a slope of zero. Use the example buttons to compare positive, negative, zero, fractional, and vertical lines without retyping coordinates.
Slope is a ratio of vertical change to horizontal change: m = rise/run = (y₂ − y₁)/(x₂ − x₁). It is also the coefficient in point-slope form y − y₁ = m(x − x₁). A positive slope means y increases as x increases, a negative slope means y decreases, and a zero slope creates a horizontal line. A vertical line has no finite slope because its run is zero.
For P₁ = (1, 2) and P₂ = (4, 8), the rise is 6 and the run is 3, so m = 2. The line through the points is y = 2x, the angle of inclination is about 63.435°, and the distance is √45. Enter the points, then compare the displayed equation and segment with your hand calculation. This same workflow works for negative, fractional, horizontal, and vertical lines.
For points (−2, 5) and (4, −7), the rise is −12 and the run is 6, so the slope is −2. Using point-slope form with (−2, 5) gives y − 5 = −2(x + 2), which simplifies to y = −2x + 1. The graph should pass through both original points and fall two units for every unit moved right.
If a line represents distance over time, slope can describe speed; if it represents cost over items, slope can describe the cost per item. The units matter: a rise of 12 dollars over a run of 3 items gives a slope of 4 dollars per item. Use the calculator’s rise, run, and angle values to connect the numerical result to the situation being modeled.
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
Subtract the first y-coordinate from the second, subtract the first x-coordinate from the second, then divide rise by run: m = (y₂ − y₁)/(x₂ − x₁).
Yes. A negative slope means the line falls as x increases.
It is undefined because the run is zero, so division by zero is not allowed.
It is zero because the y-values do not change as x changes.
No. Reversing both points changes the signs of the rise and run, so their ratio stays the same.
Use y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is either known point.
It is the angle measured counterclockwise from the positive x-axis to the line, usually reported between 0° and 180°.