# Difference Between Parabola and Line Equation ••• Comstock/Comstock/Getty Images

When you're graphing equations, each degree of polynomial creates a different sort of graph. Lines and parabolas come from two different polynomial degrees, and looking at the format can quickly tell you what kind of graph you'll end up with.

## Linear Equations

Lines come up from first-degree polynomials. The general format for a linear equation is y = mx + b. "M" refers to the slope of the line, which is the rate at which it climbs or falls. A negative slope will go down a graph as x-values decrease, and a positive slope will go up a graph as x-values increase. "B" is called the y-intercept and shows where the line crosses the y-axis.

## Plotting a Graph from the Equation

You can plot one point at the y-intercept. So, if you have the equation y = -2x + 5, you can draw a point at 5 on the y axis. Then, plug one more x-value in, such as 3. y = -2(3) + 5 gives you y = -1. So you can draw another point at (3, -1). Draw a line through those points and beyond, drawing arrows on both ends to show the line continues indefinitely.

## Parabolic Equations

Parabolas are the result of second-degree polynomials, and the general format is y = ax^2 + bx + c. The "a" indicates the width of the parabola -- the closer l a l (the absolute value of a) is to zero, the wider the arc will be. If "a" is negative, the parabola will open to the bottom; if positive, it will open to the top.

## Graphing

You can plug x-values in to find corresponding y-values, but it's trickier to graph because the parabola will curve around a vertex (the point where the parabola turns around). To find the vertex (h,k) divide the opposite of "b" by 2a. In the equation y = 3x^2 - 4x + 5, that gives you 4/3, which is the h-value. Plug h in to get k. y = 3(4/3)^2 - 4(4/3) + 5, or 48/9 - 48/9 + 5, or 5. Your vertex will be at (4/3, 5). Plug in other x-values to get points to help you draw the curving parabola.