SECTION 1.1 OBJECTIVES 1. Use the Distance Formula 2. Use the Midpoint Formula 3. Graph Equations by Hand by Plotting Points 4. Graph Equations Using a Graphing Utility 5. Use a Graphing Utility to Create Tables 6. Find Intercepts from a Graph 7. Use a Graphing Utility to Approximate Intercepts
Rectangular or Cartesian Coordinate System Rectangular Coordinat es x axis y axis origin
Let's plot the point (6,4) (-3,-5) (0,7) Let's plot the point (-6,0) (6,4) (-6,0) Let's plot the point (-3,-5) Let's plot the point (0,7) Rectangular Coordinat es
Quadrant I x > 0, y > 0 Quadrant II x < 0, y > 0 Quadrant III x < 0, y < 0 Quadrant IV x > 0, y < 0 Coordinat e Axis
Determine if the following points are on the graph of the equation - 3 x + y = 6 (b) (2, 0) (a) (0, 4) (c) (-1, 3)
Steps to Graph an Equation by Hand by Plotting Points 1. Find all points (x, y) that satisfy the equation. To determine these points, choose values of x and use the equation to find the corresponding values for y. Create a table of values. 2. Plot the points listed in the table. Now connect the points to obtain the graph of the equation.
Steps for Graphing an Equation Using a Graphing Utility 1. Solve the equation for y in terms of x 2. Enter the equation to be graphed into your graphing utility. (y= editor) 3. Choose an initial viewing window. Without any knowledge about the behavior of the graph, it is common to choose the standard viewing window as the initial viewing window. 4. Graph the equation 5. Adjust the viewing window until a complete graph is obtained
Approximating Intercepts Using a Graphing Utility 1. Use 2 nd Calc, Value on the TI-83/84 calculator to find the y-intercept by entering 0 for the x-value. 2. Use 2 nd Calc, Zero on the TI-83/84 calculator to find the x-intercept. See the owners’ manual for specific instructions. 3. For other calculators, check your owners’ manual.