Visualizing linear equations using the slope-intercept form.
- Author
- Sukesh Ashok Kumar
This example demonstrates one of the most fundamental concepts in algebra: the linear equation in slope-intercept form (y = mx + c). By plotting this equation pixel by pixel, students can see how slope and y-intercept work together.
Mathematical Concepts:
- Linear equation: y = mx + c (slope-intercept form)
- Slope (m): rate of change, rise over run (Δy/Δx)
- Y-intercept (c): where line crosses y-axis (when x=0)
- Linear relationship: constant rate of change
- For every unit increase in x, y increases by m units
In This Example:
- m = 1 (slope of 1 means 45-degree angle, rise = run)
- c = 50 (line crosses y-axis at y=50)
- Equation: y = 1×x + 50, simplified to y = x + 50
Programming Concepts:
- Translating mathematical formulas to code
- Loop iteration over domain (x values)
- Calculating dependent variable (y) from independent variable (x)
- Coordinate transformation (offsetting x by 50 for visibility)
What you'll learn:
- How slope-intercept form creates a straight line
- Why slope determines the angle of the line
- How y-intercept positions the line vertically
- Visualizing algebraic equations geometrically
- The relationship between math formulas and graphics
- How to plot continuous mathematical functions
Experiment Ideas:
- Change m to 2: steeper line (rises faster)
- Change m to 0.5: gentler slope
- Change m to -1: line going down (negative slope)
- Change c to 100: shifts line up
- Change c to 0: line passes through origin
Compile:
gcc m-linear-equation.c gfx/simplegfx.c -o output/m-linear-equation -lX11
Run:
./output/m-linear-equation
1.9.1