Presentation on theme: "Chapter 3: Parallel and Perpendicular Lines"— Presentation transcript:
1Chapter 3: Parallel and Perpendicular Lines 3-6 Lines in the Coordinate Plane
2Objectives: Student will be able: 1.To write the equations of lines in slope intercept form2.To graph lines given their equationHW/CW: pgs 169 #’s 2 – 16, Even
3Slope-Intercept Formy = mx + b m is the slopeb is the y-interceptYou need m and b to write the equation!
4Write the equation of the line. What is the y-intercept?b = -2What is m?m = 3/2y = 3/2x -2xy
5Write the equation of the line. b = ?b = 1m = ?m = -1/2y = -1/2x + 1xy
6Write the equation of the line. b = ?b = 4m = ?m = 0y = 4xy
7Find the slope and y-int. of each equation. 1) y = -4x + 3m = -4b = 32) y = 5 - 1/2xm = -1/2b = 53) 8x + y = 3/4m = -8b = 3/44) 4x - 2y = 10m = 2b = -5
8Type 1: Write the equation given the slope and y-intercept 1) m = -3, b = 1y = -3x + 12) m = -2/5, b = -4y = -2/5x - 4
9x- and y-interceptsThe 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.
10Finding 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 = 62x = 6x = 3So (3, 0) is the x-intercept of the line.
11Finding 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 = 60+y = 6y = 6So (0, 6) is the y-intercept of the line.
12To summarize…. To find the x-intercept, plug in 0 for y. To find the y-intercept, plug in 0 for x.
13Find the x- and y-intercepts of x = 4y - 5 x-intercept:Plug in y = 0x = 4y-5x = 4(0) - 5x = 0 - 5x = -5(-5, 0) is the x-int.y-intercept:Plug in x = 0x = 4y-50 = 4y - 55 = 4y5/4 = y(0, 5/4) is the y-int.
14Find the x- and y-intercepts of y = -3x – 1 x-interceptPlug in y=0y = -3x - 10 = -3x - 11 = -3x-1/3 = x(-1/3, 0) is the x-int.y-interceptPlug in x=0y = -3(0) - 1y = 0 - 1y = -1(0, -1) is the y-int.
15Find the x- and y-intercepts of 6x - 3y =-18 x-interceptPlug in y=06x-3y=-186x-3(0) = -186x - 0 = -186x = -18x = -3(-3, 0) is the x-int.y-interceptPlug in x=06x-3y=-186(0)-3y = -180 - 3y = -18-3y = -18y = 6(0, 6) is the y-int.
16Find the x- and y-intercepts of x=3 x-interceptPlug in y=0There is no y. Why?X=3 is a vertical line so x always equals 3.(3, 0) is the x-int.y-interceptA vertical line never crosses the y-axis.There is no y-int.xy
17Find the x- and y-intercepts of y=-2 x-interceptPlug in y=0Y cannot = 0 because y=-2.y=-2 is a horizontal line so it never crosses the x-axis.There is no x-int.y-interceptY=-2 is a horizontal line so y always equals -2.(0,-2) is the y-int.xy
18Graphing Equations Example: Graph the equation -5x + y = 2 Solve for y first.-5x+y=2 Add 5x to both sides.y=5x+2The 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.
20Example :Graph the equation 4x - 3y = 12. Graphing EquationsExample :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 – 4The 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.