Section 1 1 The Distance and Midpoint Formulas

y is x a • (x, y) Ordered pair (x-coordinate, y-coordinate) (abscissa, ordinate) x

Let's plot the point (6, 4) (0, 7) Let's plot the point (-6, 0)

Quadrant II x < 0, y > 0 Quadrant I x > 0, y

All graphing utilities (graphing calculators and computer software graphing packages) graph equations by plotting

You must set the scale on each axis. You must also include the smallest

Here are these settings and their relation to the Cartesian coordinate system. Copyright ©

Finding the Coordinates of a Point Shown on a Graphing Utility Screen Find the

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Horizontal or Vertical Segments Copyright © 2013 Pearson Education, Inc. All rights reserved

Find the distance d between the points (2, – 4) and (– 1, 3).

Find the midpoint of the line segment from P 1 = (4, – 2)

Graph Equations by Hand by Plotting Points Copyright © 2013 Pearson Education, Inc. All

Determine if the following points are on the graph of the equation – 3

Graph Equations Using a Graphing Utility Copyright © 2013 Pearson Education, Inc. All rights

To graph an equation in two variables x and y using a graphing utility

Expressing an Equation in the Form y = {expression in x} Solve for y:

Graphing an Equation Using a Graphing Utility Use a graphing utility to graph the

Graphing an Equation Using a Graphing Utility Step 2: Enter the equation into the

Graphing an Equation Using a Graphing Utility Step 4: Graph the equation. Step 5:

Use a Graphing Utility to Create Tables Copyright © 2013 Pearson Education, Inc. All

Create a Table Using a Graphing Utility Create a table that displays the points

Create a Table Using a Graphing Utility Step 3: Set up a table using

Use a Graphing Utility to Approximate Intercepts Copyright © 2013 Pearson Education, Inc. All

Approximating Intercepts Using a Graphing Utility Use a graphing utility to approximate the intercepts

Approximating Intercepts Using a Graphing Utility The e. VALUEate feature of a TI-84 Plus

Approximating Intercepts Using a Graphing Utility The ZERO feature of a TI-84 Plus is

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All graphing utilities (graphing calculators and computer software graphing packages) graph equations by plotting points on a screen. The screen of a graphing utility will display the coordinate axes of a rectangular coordinate system. Copyright © 2013 Pearson Education, Inc. All rights reserved

You must set the scale on each axis. You must also include the smallest and largest values of x and y that you want included in the graph. This is called setting the viewing rectangle or viewing window. Copyright © 2013 Pearson Education, Inc. All rights reserved

Finding the Coordinates of a Point Shown on a Graphing Utility Screen Find the coordinates of the point shown. Assume the coordinates are integers. Viewing Window 2 ticks to the left on the horizontal axis (scale = 1) and 1 tick up on the vertical axis (scale = 2), point is (– 2, 2) Copyright © 2013 Pearson Education, Inc. All rights reserved

To graph an equation in two variables x and y using a graphing utility requires that the equation be written in the form y = {expression in x}. If the original equation is not in this form, rewrite it using equivalent equations until the form y = {expression in x} is obtained. In general, there are four ways to obtain equivalent equations. Copyright © 2013 Pearson Education, Inc. All rights reserved

Expressing an Equation in the Form y = {expression in x} Solve for y: 2 y + 3 x – 5 = 4 We replace the original equation by a succession of equivalent equations. Copyright © 2013 Pearson Education, Inc. All rights reserved

Graphing an Equation Using a Graphing Utility Step 2: Enter the equation into the graphing utility. Step 3: Choose an initial viewing window. Copyright © 2013 Pearson Education, Inc. All rights reserved

Create a Table Using a Graphing Utility Create a table that displays the points on the graph of 6 x 2 + 3 y = 36 for x = – 3, – 2, – 1, 0, 1, 2, and 3. Step 1: Solve for y: y = – 2 x 2 + 12 Step 2: Enter the equation into the graphing utility. Copyright © 2013 Pearson Education, Inc. All rights reserved

Approximating Intercepts Using a Graphing Utility Use a graphing utility to approximate the intercepts of the equation y = x 3 – 16. Here’s the graph of y = x 3 – 16. Copyright © 2013 Pearson Education, Inc. All rights reserved

Approximating Intercepts Using a Graphing Utility The e. VALUEate feature of a TI-84 Plus graphing calculator accepts as input a value of x and determines the value of y. If we let x = 0, the y-intercept is found to be – 16. Copyright © 2013 Pearson Education, Inc. All rights reserved

Approximating Intercepts Using a Graphing Utility The ZERO feature of a TI-84 Plus is used to find the x-intercept(s). Rounded to two decimal places, the x-intercept is 2. 52. Copyright © 2013 Pearson Education, Inc. All rights reserved