Equation of a Line - Slope-Intercept Form
y = mx + b
Above is a program that will help you visualize how changing the values for the slope, m, and the y-intercept, b, will affect the graph of the equation y = mx + b. At first the program will be automatically cycling through several values for m and b. If you want to use the sliders to control it yourself, just press the 'You Control' button.
Notice that when the slope, m, is positive, the line slants upward to the right. The more positive m is, the steeper the line will slant upward to the right.
When the slope is negative, the line slants downward to the right, and, as the slope becomes more and more negative, the line will slant downward steeper and steeper to the right.
Also, notice that when the y-intercept, b, is positive, the line crosses the y-axes above y = 0. When b is negative, the line crosses the y-axis somewhere below y = 0. In fact, b is the value on the y-axis where the line passes through this axis. The line intercepts, or crosses, the y-axis here, and, therefore, b is called the y-intercept.
Summary of Details
This linear function:
f(x) = mx + b
May be graphed on the x, y plane as this equation:
y = mx + b
- This equation is called the slope-intercept form for a line.
- The graph of this equation is a straight line.
- The slope of the line is m.
- The line crosses the y-axis at b.
- The point where the line crosses the y-axis is called the y-intercept.
- The x, y coordinates for the y-intercept are (0, b).