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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:**

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

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

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**Write the equation of the line.**

What is the y-intercept? b = -2 What is m? m = 3/2 y = 3/2x -2 x y

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**Write the equation of the line.**

b = ? b = 1 m = ? m = -1/2 y = -1/2x + 1 x y

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**Write the equation of the line.**

b = ? b = 4 m = ? m = 0 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 = 5 - 1/2x 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 = -2/5x - 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 = 0 - 5 x = -5 (-5, 0) is the x-int. y-intercept: Plug in x = 0 x = 4y-5 0 = 4y - 5 5 = 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 - 1 0 = -3x - 1 1 = -3x -1/3 = x (-1/3, 0) is the x-int. y-intercept Plug in x=0 y = -3(0) - 1 y = 0 - 1 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 = -18 0 - 3y = -18 -3y = -18 y = 6 (0, 6) is the y-int.

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**Find the x- and y-intercepts of x=3**

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. y-intercept A vertical line never crosses the y-axis. There is no y-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=2 Add 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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1. Graph y=5x+2 x y

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**Example :Graph the equation 4x - 3y = 12.**

Graphing Equations Example :Graph the equation 4x - 3y = 12. Solve for y first. 4x-3y=12 Subtract 4x from both sides. -3y = -4x 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.

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

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Finding x- and y-intercepts algebraically

Finding x- and y-intercepts algebraically

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