How to Graph Linear Equations

Are you stuck not knowing how to draw a linear equation without using a calculator? Luckily, drawing a graph of a linear equation is pretty simple! All you need to know is a couple things about your equation and you're good to go. Let's get started!

Steps

  1. Image titled Graph Linear Equations Step 1
    1
    Make sure the linear equation is in the form y = mx + b. This is called the y-intercept form, and it's probably the easiest form to use to graph linear equations. The values in the equation do not need to be whole numbers. Often you'll see an equation that looks like this: y = 1/4x + 5, where 1/4 is m and 5 is b.
    • m is called the "slope," or sometimes "gradient." Slope is defined as rise over run, or the change in y over the change in x.
      Image titled Graph Linear Equations Step 1Bullet1
    • b is defined as the "y-intercept." The y-intercept is the point at which the line crosses the Y-axis.
      Image titled Graph Linear Equations Step 1Bullet2
    • x and y are both variables. You can solve for a specific value of x, for example, if you have a y point and know the m and b values. x, however, is never merely one value: its value changes as you go up or down the line.
      Image titled Graph Linear Equations Step 1Bullet3
  2. 2
    Plot the b number on the Y-axis. Your b is always going to be a rational number. Just whatever number b is, find its equivalent on the Y-axis, and put the number on that spot on the vertical axis.

    • For example, let's take the equation y = 1/4x + 5. Since the last number is b, we know that b equals 5. Go 5 points up on the Y-axis and mark the point. This is where your straight line will pass through the Y-axis.
      Image titled Graph Linear Equations Step 2Bullet1
  3. Image titled Graph Linear Equations Step 3
    3
    Convert m into a fraction. Often, the number in front of x is already a fraction, so you won't have to convert it. But if it isn't, convert it by simply placing the value of m over 1.
    • The first number (numerator) is the rise in rise over run. It's how far the line travels up, or vertically.
      Image titled Graph Linear Equations Step 3Bullet1
    • The second number (denominator) is the run in rise over run. It's how far the line travels to the side, or horizontally.
      Image titled Graph Linear Equations Step 3Bullet2
    • For example:
      • A 4/1 slope travels 4 points up for every 1 point over.
      • A -2/1 slope travels 2 points down for every 1 point over.
      • A 1/5 slope travels 1 points up for every 5 points over.
  4. Image titled Graph Linear Equations Step 4
    4
    Start extending the line from b using slope, or rise over run. Start at your b value: we know that the equation passes through this point. Extend the line by taking your slope and using its values to get points on the equation.
    • For example, using the illustration above, you can see that for every 1 point the line rises up, it travels 4 to the right. That's because the slope of the line is 1/4. You extend the line indefinitely along both sides, continuing to use rise over run to graph the line.
    • Whereas positive-value slopes travel upward, negative-value slopes travel downward. A slope of -1/4, for example, would travel down 1 point for every 4 points it travels to the right.
  5. Image titled Graph Linear Equations Step 5
    5
    Continue extending the line, using a ruler and being sure to use the slope, m, as a guide. Extend the line indefinitely and you're done graphing your linear equation. Pretty easy, isn't it?

Article Info

Categories: Algebra