Chapter 3 Lesson 5 Objective To write equations

Chapter 3 Lesson 5 Objective: To write equations of lines.

point-slope form: for a nonvertical line through point (x 1, y 1) with slope m is y-y 1=m(x-x 1). Example 1: Using Point-Slope Form Write an equation of the line through point P(-1, 4) with slope 3. y-y 1=m(x-x 1) Use point-slope form Y-4=3[x-(-1)] Substitute 3 for m and ( -1, 4) for (x 1, y 1). Y-4=3(x+1) Simplify

Example 2: Using Point-Slope Form Write an equation of the line through point P(2, -4) with slope -1. y-y 1=m(x-x 1) Use point-slope form Y-(-4)=-1(x-2) Substitute -1 for m and ( 2, -4) for (x 1, y 1). Y+4=-1(x-2) Simplify Example 3: Using Point-Slope Form Write an equation of the line through point P(3, -6) with slope -8. y-y 1=m(x-x 1) Use point-slope form Y-(-6)=-8(x-3) Substitute -8 for m and ( 3, -6) for (x 1, y 1). Y+6=-8(x-3) Simplify

Example 4: Writing an Equation of a Line Given Two Points Write an equation of the line through A(-2, 3) and B(1, -1). Step 1: Find the slope. y 2 -y 1 m= x -x 2 1 -1 -3 m= 1 -(-2) -4 m= 3 Step 2: Select one of the points. Write an equation in point-slope form. y-y 1=m(x-x 1) Y-3=(-4/3)[x-(-2)] Y-3=(-4/3)(x+2)

Example 5: Writing an Equation of a Line Given Two Points Write an equation of the line through A(4, -9) and B(-1, 1). Step 1: Find the slope. y 2 -y 1 m= x -x 2 1 1 -(-9) m= -1 -4 10 m= -5 m= -2 Step 2: Select one of the points. Write an equation in point-slope form. y-y 1=m(x-x 1) Y-(-9)=(-2)(x-4) Y+9=(-2)(x-4) y-y 2=m(x-x 2) Y-1=(-2)(x-(-1)) Y-1=(-2)(x+1)

Example 6: Equations of Horizontal and Vertical Lines Write equations for the horizontal line and the vertical line that contain P(3, 2). Every point on the horizontal line through P(3, 2) has a y-coordinate of 2. It crosses the y-axis at (0, 2). The equation of the line is y = 2. Every point on the vertical line through P(3, 2) has an x-coordinate of 3. It crosses the x-axis at (3, 0). The equation of the line is x=3. P(3, 2) 2 -2 -2 -4 -6 2 4 6

Homework Page 155 -157 #17 -32; 39 -44; 47; 52