2. One method of graphing a linear equation is to construct a table of values. Example: Consider the equation y = 2x + 3 xy 1 03 15 27 39 When x = 0, y = 3 When increasing x by 1, we seem to increase y by 2

3. The table and graph suggest another method of graphing a linear equation. This method is based on two numbers. The SLOPE This is the coefficient of x when the equation is in the from y = mx + b. In this case, the slope is 2. The y - INTERCEPT This is the value of y when x = 0. In this case, the y-intercept is 3 y = 2x + 3 Slope y - intercept The graph of the equation y = mx + b has slope m and y-intercept b.

4. The equation y = mx + b is called the slope y - intercept form of the equation of a line. We can draw the graph of an equation in this form without making a table of values. EXAMPLE 1: EXAMPLE 1: Graph this equation: y = -2x +4 Solution: y - intercept is +4 Point (0, 4) Slope = -2 Begin at Point (0,4) and use the slope to draw one point above and one point below the starting point.

5. Find the equations of the lines shown on the grid. SOLUTION: L 1 has a slope of 1 and y-intercept of 2 Therefore its equation is y = x + 2 L 2 has a slope of and a y-intercept of -1 Therefore its equation is y = x -1 -3 2 -3 2

6. Find the equations of the lines shown on the grid.

7. SOLUTION: L 1 has a slope of and y-intercept of 1 Therefore its equation is y = x + 1 L 2 has a slope of and a y-intercept of -2 Therefore its equation is y = x - 2 1212 1212 -3 4 -3 4

8. Answer the following questions. Question 1: State the slope and y-intercept for these lines. a)y = 3x + 5 b)y = -2x + 3 c)y = x - 2 4343 Question 2: Write the equation of the line that has: a)m = 2, b = 3 b)m = -1, b = 4 c)m =, b = 0 2323

9. Answer the following questions. Question 1: State the slope and y-intercept for these lines. a)y = 3x + 5 b)y = -2x + 3 c)y = x - 2 4343 Question 2: Write the equation of the line that has: a)m = 2, b = 3 b)m = -1, b 4 c)m =, b = 0 2323 Slope = 3, y-int = 5 Slope = -2, y-int = 3 Slope =, y-int = -2 4343 y = 2x + 3 y = -x + 4 y = x 2323

10. For each line, state the slope, the y-int., and the equation.

11. m = y - int = 1 Equation = y = x + 1 1212 1212 m = -2 y - int = 1 Equation = y = -2x + 1

12. CLASS WORK Finish Lesson 9(3) Check solutions to Lesson 9(3) Copy notes and examples from Lesson 9(4) Do Lesson 9(4) worksheet.