1 What you will learn today 1. Review of slope 2. How to determine slope 3. How to graph a linear equation in y = mx + b form 4. Slopes of parallel and perpendicular lines 5. How to graph a linear equation in standard form

Objective: 2.2 Slope and 2.3 Quick Graphs 2 Fun with Slope Slope is the ratio of vertical change to horizontal change – rise over run.

Objective: 2.2 Slope and 2.3 Quick Graphs 3 Finding Slope 1. Look at the graph and “count” the vertical change over the horizontal change. 2. Use the formula for finding slope: Where you have two points (x 1, y 1 ) (x 2, y 2 )

Objective: 2.2 Slope and 2.3 Quick Graphs 4 Finding Slope Using the Formula  Example: Find the slope of a line passing through (-3, 5) and (2, 1)

Objective: 2.2 Slope and 2.3 Quick Graphs 5 You Try  Find the slope of the line passing through (-2, -4) and (3, -1)

Objective: 2.2 Slope and 2.3 Quick Graphs 6 Types of Slope Positive m > 0 negative m<0 no slope m = 0 Undefined slope

Objective: 2.2 Slope and 2.3 Quick Graphs 7 Classifying Lines Using Slope  Example: Without graphing tell whether the line through the given points rises, falls, is horizontal, or is vertical. a. (3, -4), (1, -6)b. (2, -1), (2, 5)

Objective: 2.2 Slope and 2.3 Quick Graphs 8 Comparing Steepness of Lines Example: Tell which line is steeper: Line 1: through (2,3) and (4,7) or Line 2: through (-1,2) and (4,5)

Objective: 2.2 Slope and 2.3 Quick Graphs 9 Parallel and Perpendicular Lines Parallel lines have slopes that are equal. Perpendicular lines have slopes that are the negative reciprocal of one another (e.g. 2 and - 1/2)

Objective: 2.2 Slope and 2.3 Quick Graphs 10 Parallel or Perpendicular  Example: Tell whether the lines are parallel, perpendicular, or neither. a. Line 1 through (-3, 3) and (3, 1) Line 2 through (-2,-3) and (2,3) You Try: Line 1 through (1,-2) and (3,-2) Line 2 through (-5,4) and (0,4)

Objective: 2.2 Slope and 2.3 Quick Graphs 11 Graphing Using the Slope-Intercept Form y = mx + b is the slope intercept form of a linear equation. b is the y-intercept (the place where the line crosses the y-axis) m is the slope.

Objective: 2.2 Slope and 2.3 Quick Graphs 12 Steps for Graphing in Slope Intercept Form 1. Put the equation in slope-intercept form. 2. Find the y-intercept and use it to plot the point where the graph crosses the y-axis. 3. Find the slope in the equation and use it to “count” to a second point. 4. Draw a line through the two points

Objective: 2.2 Slope and 2.3 Quick Graphs 13 Example  Graph y = 3/4x – 2 1. it is in slope intercept form. 2. y-intercept is the slope is ¾ 4. connect the dots

Objective: 2.2 Slope and 2.3 Quick Graphs 14 You Try  Graph y = 1/2x + 1

Objective: 2.2 Slope and 2.3 Quick Graphs 15 A Real World Example  You are buying an $1100 computer on layaway. You make a $250 deposit and then make weekly payments according the equation a = 850 – 50t where a is the amount you own and t is the number of weeks. Step 1: rewrite as a = -50t Step 2: y-intercept is 850 Step 3: slope is -50 Step 4: connect the dots

Objective: 2.2 Slope and 2.3 Quick Graphs 16 Using the Standard Form to Graph an Equation The standard form of a linear equation is Ax + By = C. We will use the x and y intercepts to graph these types of equations.

Objective: 2.2 Slope and 2.3 Quick Graphs 17 The Steps Step 1: Put the equation in standard form Step 2: Set y equal to zero and solve for x to get the x-intercept. Step 3: Set x equal to zero and solve for y to get the y-intercept. Step 4: Draw a line through the two points.

Objective: 2.2 Slope and 2.3 Quick Graphs 18 Example  Graph 2x + 3y = 12

Objective: 2.2 Slope and 2.3 Quick Graphs 19 Horizontal and Vertical Lines  The graph of y = some number is a horizontal line through (0, the number).  The graph of x = some number is a vertical line through (the number, 0).

Objective: 2.2 Slope and 2.3 Quick Graphs 20 Example  Graph y = 3  Graph x = -2

Objective: 2.2 Slope and 2.3 Quick Graphs 21 Homework  Page 79, 18, 22, 24, 26, 27, all, 41, 42, 44, 46  Page 86, all,20, 26, 34, all, 44, 52