Lesson 3.5 Essential Question: How can you describe the graph of the equation y=mx+b? `Objectives: Finding the slope of a line Finding the slope of a line.

Presentation on theme: "Lesson 3.5 Essential Question: How can you describe the graph of the equation y=mx+b? `Objectives: Finding the slope of a line Finding the slope of a line."— Presentation transcript:

1 Lesson 3.5 Essential Question: How can you describe the graph of the equation y=mx+b? `Objectives: Finding the slope of a line Finding the slope of a line from a table Identifying slopes and Y-intercepts Using Slope-intercept form to graph linear equations

2 The rate of change between any two points on a line.
Vocabulary: SLOPE: The rate of change between any two points on a line. The measure of the steepness of a line To find the slope of a line, find the ratio of the change in y (the vertical change – rise) to the change in x (the horizontal change – run) Change in y Y2 – Y1 Slope = = Change in x X2 – X1

3 :Find the slope of a Line
Examples: The line rises from left to right so the slope is positive Let (X1,Y1) = (-3,-2) and let (X2,Y2) = (3,2) The line falls from left to right so the slope is negative Let (X1,Y1) = (0,2) and let (X2,Y2) = (2,-1) Y2 – Y1 2 – (-2) 4 2 Y2 – Y1 -1 – 2 -3 m= = = = m= = = X2 – X1 3 – (-3) 6 3 X2 – X1 2 – (0) 2

4 Find the slope from a table
c. x f(x) 4 20 7 14 10 8 13 2 x f(x) -1 2 1 3 5 x f(x) -3 6 9 Choose any two points from table a. Use the points in the slope formula Let (X1,Y1) = (4,20) and let (X2,Y2) = (10,8) Choose any two points from table b. Use the points in the slope formula Let (X1,Y1) = (3,2) and let (X2,Y2) = (5,2) Y2 – Y1 8 –20 -12 -2 Y2 – Y1 2 – 2 m= = = = m= = = or 0 X2 – X1 10 – 4 6 1 X2 – X1 5 – 3 2 Choose any two points from table c. Use the points in the slope formula Let (X1,Y1) = (-3,-3) and let (X2,Y2) = (-3,6) Y2 – Y1 6 – (-3) 9 or undefined m= = = X2 – X1 -3 – (-3)

5 Objective #2: Finding slope from a table (continued)
The line rises from left to right Positive Slope: The line falls from left to right Negative Slope: The line is horizontal (constant function) Slope of 0: Undefined Slope: The line is vertical

6 Identifying slopes and Y-intercepts
Slope-Intercept form y = m x + b y-- intercept slope Standard form Rewrite into Slope-Intercept form Isolate y Re-write each standard form equation in slope-intercept form: 1) -4x + y = -4 2) 3x + y = 5 3) -9x - 3y = 6 y = 4x – 4 y = - 3x + 5 y = -3x – 2

7 Using Slope-intercept form to graph linear equations
Identify the intercepts Graph: 2x + y = 2 Re-write in slope-intercept form x y y = - 2x + 2 Find the y intercept y = -2 (0) +2 1 (0 , 2) - 2 Find the slope and the y intercept m = -2 and b = 2

8 Review what was taught and Write your summary