Graphing Linear Equations

Chapter Sections 7.1 – The Cartesian Coordinate System and Linear Equations in Two Variables 7.2 – Graphing Linear Equations 7.3 – Slope of a Line 7.4 – Slope-Intercept and Point-Slope Forms of a Linear Equation 7.5 – Graphing Linear Inequalities 7.6 – Functions Chapter 1 Outline

Graphing Linear Equations

Graph by Plotting Points Solve for y: Solve the linear equation for the variable y. That is, get y by itself on the left side of the equation. Substitute a number in for x: Select a number and substitute it into the equation for x and find the corresponding value for y. Record the ordered pair (x,y). Repeat step 2: Select two different values of x. This will give you two additional ordered pairs. Plot the points: Plot the three ordered pairs. The three points should be collinear. If they are not, recheck your work. Draw the line: Draw a straight line through the points.

Graph by Plotting Points Graph the equation y = 2x + 4. Let x = -1 y = –2 + 4 y = 2 This give us the point (-1, 2). Let x = 0 y = 0 + 4 y = 4 This give us the point 0, 4). Let x = 1 y = 2 + 4 y = 6 This give us the point (1, 6). Plot the points and draw the line.

Graph by Plotting Points Plot the points (-1, 2), (0, 4), and (1, 6). Draw the line.

Graph Using Intercepts Find the y-intercept by setting x equal to 0 and finding the corresponding value of y. Find the x-intercept by setting the y equal to 0 and finding the corresponding value of x. Determine a checkpoint by selecting a nonzero value for x and finding the corresponding y. Plot the two intercepts and the check point. Draw a straight line through the points.

Graph Using Intercepts Graph the equation 3y = 6x + 12. Let x = 0 3y = 6(0) + 12 y = 4 This gives us the y-intercept (0, 4). Let y = 0 -3(0) = 6x + 12 x = -2 This gives us the x-intercept (-2, 0). y =8 Let x = 2 3y = 6(2) + 12 3y = 24 This gives us the point (2, 8) Plot the points and draw the line.

Graph by Plotting Points Plot the points (-2, 0), (0, 4), and (2, 8). Draw the line.