Graphing linear equationsBefore graphing linear equations, make sure you understand the concepts of graphing slope since it is very similar. The standard form of a linear equation is y = mx + b m is the slope. b is the yintercept (the yintercept is a point on the yaxis) Follow the following guidelines to graph a linear equation: Method 1 Step #1: Put the yintercept on the coordinate system. Step #2: Starting from the yintercept, use the slope to locate one more point on the coordinate system Step #3: Draw a line between the yintercept and the other point Example #1: Graph y = (4/3)x + 2 Step #1: Here m = 4/3 and b = 2. Put 2 on the coordinate system. The graph is below and the yintercept is shown with a red dot. Step #2: Starting from the 2, go up 4 units (you end up at 6, where the black dot is) and over 3 units (The new point is shown with a blue dot) Notice that we move to the right. We always move to the right! Step #3: Draw a line between the red dot and the blue dot. See below: Example #2: Graph y = (4/3)x + 2 Same problem with the exception that the slope is negative. Step #1 stays the same. In step #2, you go down 4 units instead of going up. We always go down when the slope is negative, but again we still move to the right In step #3, after you go down 4 units and move to the right 3 units, the point will be located at (3, 4) Draw a line between that point and the red dot. Example #3: Graph y = x − 2 Rewrite the equation as y = 1x + 2 Here m = 1 and b = 2. Repeat step #1 through #3 Method 2 Method 2 consists of looking for points, at least 2 or 3, plotting them, and drawing a straight line between them It is common practice to look for the yintercept, xintercept, and any other point by letting x be anything and solve for y Example #4: Graph y = 2x + 4 yintercept: When x = 0, y = 2 × 0 + 4 = 0 + 4 = 4 ( Notice that x is always zero when a point is on the yaxis) The point is (0, 4) shown with a green dot xintercept: When y = 0, 0 = 2x + 4 ( Notice that y is always zero when a point is on the xaxis and xintercept is a point on the xaxis) So 0 = 2x + 4 0 + 4 = 2x + 4 + 4 4 = 2x 4/2 = (2/2)x 2 = x The point is (2, 0) shown with a brown dot At this point, you could make the graph with these 2 points when graphing linear equations, but it will not hurt to get one more So as we said, let x be anything, say 4, then y = 2 × 4 + 4 = 8 + 4 = 4 The third point is (4, 4) shown in red. The graph is shown below The two methods above are used when graphing linear equations. Study them carefully! 




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