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Linear Functions: How to Graph

Graphing equations allows us to have a better understanding of an equation, and what it represents. Let's look at the example below:


Graph the equation y = .5x + 1


Step 1: Plot the y-intercept. Remember that in the equation y = mx +b, b is the y-intercept. Also remember that the y-intercept is the point on the graph where x = 0. In this example, the y-intercept is at (0,1).


Step 2: Use the rate of change (m) to plot points. In this equation, the rate of change, m, is .5 (or 1/2). This means that for every one it goes up, it must go two right. Knowing this, start at the y-intercept and go up one, right two, and plot the point there. Do this as many times as you want (as you get more comfortable with graphing, you won't need to plot as many points).


After this, go back to the y-intercept. To find points in the opposite direction, count down one, left two, and plot points as you go.


Step 3: Draw a line through all the points, extend it, and draw an arrow on either end.


Now try some practice problems on your own: (You can do this by printing out graph paper or drawing your own coordinate plane and estimating!)

1) Graph the equation: y = 3x - 1

2) Graph the equation: y = -2x + 3

3) Graph the equation: y = .75x - 2


Answers:


1) Graph: