2. © William James Calhoun, 2001 OBJECTIVE: You will graph a line given any linear equation. In the last chapter, we learned how to graph lines. Basically, you were taught to: (1) solve the linear equation for y, (2) choose three x-values (domains) (3) plug those values into the solved equation from (1), (4) plot the resulting ordered pairs, and (5) draw the line through those points with arrows on the ends. In this section, we will look at two other ways to graph lines. Neither method is more accurate. The first you will use most of the time. The second method is used only when an equation is already in standard form. 6-5: Graphing Linear Equations

3. © William James Calhoun, 2001 6-5: Graphing Linear Equations EXAMPLE 1: Graph y - 1 = 3(x + 2). (1) Solve the equation for y to get it in slope-intercept form. Add 1 to both sides. intercept slope (2) Identify the slope and y-intercept. (4) To get the next point, use the slope (in fraction form) which says to: go up 3 and right one. (5) Draw the line through the two points. (3) Plot the intercept. Distribute the 3. y - 1 = 3x + 6 +1 y = 3x + 7

4. © William James Calhoun, 2001 6-5: Graphing Linear Equations EXAMPLE 2: Graph (1) Solve the equation for y to get it in slope-intercept form. Subtract from both sides. Multiply both sides by 2. intercept slope (2) Identify the slope and y-intercept. (4) To get the next point, use the slope which says to: go down 3 and right two. (5) Draw the line through the two points. (3) Plot the intercept.

5. © William James Calhoun, 2001 6-5: Graphing Linear Equations EXAMPLE 3: Graph 2x + 5y = 20. (1) Find the x-intercept. 2x + 5(0) = 20 2x = 20 x = 10 (2) Plot it. (3) Find the y-intercept. 2(0) + 5y = 20 5y = 20 y = 4 (4) Plot it. (5) Draw the line through the two points. The next example shows an easier way to graph linear equations ONLY IF THEY ARE ALREADY IN STANDARD FORM.

6. © William James Calhoun, 2001 6-5: Graphing Linear Equations You have now learned three different ways to graph linear equations. The first way was creating a chart, choosing domains, finding ranges, plotting three points, and drawing a line. You do not need to use this method any more. The second way only works when the equation is in standard form. Find the intercepts, plot them, then draw the line. The third way will be your most-used method. (1) Solve the equation for y. (2) Determine your slope and y-intercept. (3) Plot the y-intercept. (4) Use the slope to plot the next point on the graph. (5) Draw the line through those two points. Now for a “tricky” example. Hint: its one long sucker.

7. © William James Calhoun, 2001 6-5: Graphing Linear Equations EXAMPLE 4: Graph (1) Solve the equation for y. -2y 8x - 6y = 30x - 50 -8x - 6y = 22x - 50 - 6 -6 (5) Draw the line through the two points. (3) Plot the intercept. Because of the fraction, you have to plot in-between the grid lines. Just do your best. (4) Go down eleven and right three to get next point. intercept slope (2) Identify the slope and y-intercept.

8. © William James Calhoun, 2001 6-5: Graphing Linear Equations HOMEWORK Page 359 #15 - 33 odd