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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

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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.

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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.

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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

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Find the equations of the lines shown on the grid.

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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

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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

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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

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

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

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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.

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0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 Straight Line Graphs m gives the gradient of the line and.

0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 Straight Line Graphs m gives the gradient of the line and.

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