Linear Function Grapher

About the Linear Function Grapher

Plot linear functions of the form y = mx + b. Change the slope m and intercept b to see how the line moves.

How to use this calculator

1. Enter the slope \(m\), which tells how steep the line is.
2. Enter the y-intercept \(b\), which is the starting value when \(x = 0\).
3. Use the graph to see the line rise, fall, or stay flat.
4. Check a few points on the line to confirm the pattern matches \(y = mx + b\).

The formula explained

The formula \(y = mx + b\) computes the output value \(y\) for any input \(x\). It gives a straight line because the change in \(y\) is constant for each 1-step change in \(x\).

• x = the input value on the horizontal axis
• y = the output value on the vertical axis
• m = the slope, or rate of change
• b = the y-intercept, where the line crosses the y-axis

Step by step method

1. Start with the y-intercept, so plot the point \((0, b)\).
2. Use the slope \(m\) as rise over run, then move from the intercept to find another point.
3. Draw the straight line through the points and extend it across the graph.

Worked example

Problem. Graph the linear function \(y = 2x - 3\).

1. The y-intercept is \(-3\), so plot \((0, -3)\).
2. The slope is \(2\), which means rise 2 and run 1, so from \((0, -3)\) move to \((1, -1)\).
3. Draw a straight line through the points and extend it, the graph is the line \(y = 2x - 3\).

Tips and common mistakes

• If the line is going up as you move left to right, the slope is positive. If it is going down, the slope is negative.
• Do not confuse the y-intercept \(b\) with the slope \(m\), because they play different roles in the graph.

Frequently asked questions