Linear Functions and Equations, Slope-Intercept Form

Linear function interactive app (explanation below):

Here we have an application that let's you change the slope and y-intercept for a line on the (x, y) plane. You change these values by clicking on the '+' and '-' buttons. After each click the graph will be redrawn and the equation for the line will be redisplayed using the new values.

This is an . Click the 'Show system' checkbox to expose the EZ Math Movie language. You do not have to understand EZ Math Movie to use this application.

Show system Learn about this at EZ Math Movie [ezmathmovie.com]

// Prepare graph.
setupGraph();

// Get slope from 1st input.
m = get1stInputValue();
// Get y-intercept from 2nd input.
b = get2ndInputValue();

// Find left-most y-coordinate.
y1 = (m * worldXMin) + b;
// Find right-most y-coordinate.
y2 = (m * worldXMax) + b;

// Draw line from left edge to right edge.
drawLineSegment(worldXMin, y1, worldXMax, y2);

// Display slope-intercept form.
displayEquation(m, b);

// Do this only once.
// Go again upon input.
stop();

y = mx + b

The formula y = mx + b is said to be a linear function. That means the graph of this function will be a straight line on the (x, y) plane.

One could express this as a formal function definition with notation such as:

f(x) = mx + b

Since we will be graphing (x, y) points, though, we will do our thinking with the 'y = mx + b' form for a while.

When the function for a line is expressed this way, we call it the 'slope-intercept form'.