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Chapter 3: Parallel and Perpendicular Lines 3-6 Lines in the Coordinate Plane

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Objectives: Student will be able: 4 1.To write the equations of lines in slope intercept form 4 2.To graph lines given their equation 4 HW/CW: pgs 169 #s 2 – 16, Even

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Slope-Intercept Form 4 y = mx + b m is the slope 4 b is the y-intercept 4 You need m and b to write the equation!

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Write the equation of the line. 4 What is the y- intercept? 4 b = -2 4 What is m? 4 m = 3/23/2 4 y = 3 / 2 x -2 x y

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Write the equation of the line. 4 b = ? = 1 4 m = ? = -1 / 2 4 y = -1 / 2 x + 1 x y

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Write the equation of the line. 4 b = ? = 4 4 m = ? = 0 4 y = 4 x y

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Find the slope and y-int. of each equation. 1) y = -4x + 3 m = -4 b = 3 2) y = / 2 x m = -1 / 2 b = 5 3) 8x + y = 3 / 4 m = -8 b = 3 / 4 4) 4x - 2y = 10 m = 2 b = -5

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Type 1: Write the equation given the slope and y-intercept 1) m = -3, b = 1 y = -3x + 1 2) m = - 2 / 5, b = -4 y = - 2 / 5 x - 4

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x- and y-intercepts The x-intercept is the point where a line crosses the x-axis. The general form of the x-intercept is (x, 0). The y-coordinate will always be zero. The y-intercept is the point where a line crosses the y-axis. The general form of the y-intercept is (0, y). The x-coordinate will always be zero.

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Finding the x-intercept For the equation 2x + y = 6, we know that y must equal 0. What must x equal? Plug in 0 for y and simplify. 2x + 0 = 6 2x = 6 x = 3 So (3, 0) is the x-intercept of the line.

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Finding the y-intercept For the equation 2x + y = 6, we know that x must equal 0. What must y equal? Plug in 0 for x and simplify. 2(0) + y = 6 0+y = 6 y = 6 So (0, 6) is the y-intercept of the line.

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To summarize…. To find the x-intercept, plug in 0 for y. To find the y-intercept, plug in 0 for x.

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Find the x- and y-intercepts of x = 4y - 5 x-intercept: Plug in y = 0 x = 4y-5 x = 4(0) - 5 x = x = -5 (-5, 0) is the x-int. y-intercept: Plug in x = 0 x = 4y-5 0 = 4y = 4y 5/4 = y (0, 5/4) is the y-int.

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Find the x- and y-intercepts of y = -3x – 1 x-intercept Plug in y=0 y = -3x = -3x = -3x -1/3 = x (-1/3, 0) is the x-int. y-intercept Plug in x=0 y = -3(0) - 1 y = y = -1 (0, -1) is the y-int.

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Find the x- and y-intercepts of 6x - 3y =-18 x-intercept Plug in y=0 6x-3y=-18 6x-3(0) = -18 6x - 0 = -18 6x = -18 x = -3 (-3, 0) is the x-int. y-intercept Plug in x=0 6x-3y=-18 6(0)-3y = y = y = -18 y = 6 (0, 6) is the y-int.

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Find the x- and y-intercepts of x=3 y-intercept A vertical line never crosses the y-axis. There is no y-int. x-intercept Plug in y=0 There is no y. Why? X=3 is a vertical line so x always equals 3. (3, 0) is the x-int. x y

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Find the x- and y-intercepts of y=-2 x-intercept Plug in y=0 Y cannot = 0 because y=-2. y=-2 is a horizontal line so it never crosses the x-axis. There is no x-int. y-intercept Y=-2 is a horizontal line so y always equals -2. (0,-2) is the y-int. x y

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Graphing Equations Example: Graph the equation -5x + y = 2 Solve for y first. -5x+y=2Add 5x to both sides. y=5x+2 The equation y=5x+2 is in slope-intercept form, y=mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.

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x y 1. Graph y=5x+2

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Example :Graph the equation 4x - 3y = 12. Solve for y first. 4x-3y=12 Subtract 4x from both sides. -3y = -4x + 12 Divide by -3. y = -4/-3 x+ 12/-3. Simplify. y = 4/3 x – 4 The equation y=4/3 x - 4 is in slope-intercept form, y=mx+b. The y-intercept is -4 and the slope is 4/3. Graph the line on the coordinate plane. Graphing Equations

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2. Graph y=4/3 x - 4 x y

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