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Linear Function Grapher

Define the line by

Try an example

Equation

y=2x−1y = 2x - 1
Slope
2 (rising)
y-intercept
(0, -1)
x-intercept
(1/2, 0)
Angle with the x-axis
63.43°
Perpendicular slope
-1/2

Graph

-10-8-6-4-20246810-20-1001020
y = 2x - 1

Graph a straight line from its slope and intercept, from two points, or from the standard form Ax + By = C. See the equation in slope-intercept form, both intercepts, the angle with the x-axis and the slope of a perpendicular line.

Formula

y=mx+b\text{y} = \text{mx} + \text{b}
m=(y2−y1)/(x2−x1)\text{m} = (\text{y}_{2} - \text{y}_{1}) / (\text{x}_{2} - \text{x}_{1})
b=y1−m⋅x1\text{b} = \text{y}_{1} - \text{m}·\text{x}_{1}
Ax+By=C gives m=−A/B and b=C/B\text{Ax} + \text{By} = \text{C gives m} = - \text{A}/\text{B and b} = \text{C}/\text{B}

Worked Example

Slope2
Intercept-1
Result: Line crosses y-axis at -1 and rises 2 units per 1 unit in x

Positive slope indicates upward trend; intercept anchors the line’s vertical position at x = 0.

Frequently Asked Questions

How do I interpret slope in real-world data?

Slope represents the expected change in y for each one-unit increase in x, useful for rate-based interpretation.

What does a zero slope mean?

A zero slope means y is constant across x, so the graph is a horizontal line.

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