11.2.2. Graph a Linear Equation by Plotting Points

Graph a Linear Equation by Plotting Points

There are several methods that can be used to graph a linear equation. The method we used previously was called plotting points, or the Point-Plotting Method.

• Even though it only takes two points to determine a line, it is a good habit to use three points. If you plot only two points and one of them is incorrect, you can still draw a line but it will not represent the solutions to the equation. It will be the wrong line. Three points is very good at telling you something is wrong and to recheck your work.

When an equation includes a fraction as the coefficient of x, we can substitute any numbers for x. But the math is easier if we make ‘good’ choices for the values of x. This way we will avoid fraction answers, which are hard to graph precisely.

• A common way to work with fraction coefficients is to use multiples of the denominator, in order to turn the fraction into an integer for graphing purposes.

• Sometimes its not always the case that we find a solution that is easy to graph (i.e. 2x + y = 3 → x = 3/2)
  • While we could graph this point, it is hard to be precise graphing fractions. If you solve the equation for y, it will be easier to find three solutions to the equation.
  • 2x + y = 3 → y = -2x + 3
    • Now we can choose values for x that will give coordinates that are integers.