Objective: To write equations of lines.

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Presentation transcript:

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

Using Point-Slope Form point-slope form: for a nonvertical line through point (x1,y1) with slope m is y-y1=m(x-x1). Example 1: Using Point-Slope Form Write an equation of the line through point P(-1,4) with slope 3. y-y1=m(x-x1) Use point-slope form Y-4=3[x-(-1)] Y-4=3(x+1) Substitute 3 for m and ( -1,4) for (x1,y1). Simplify

Example 2: Using Point-Slope Form Write an equation of the line through point P(2,-4) with slope -1. y-y1=m(x-x1) Use point-slope form Y-(-4)=-1(x-2) Y+4=-1(x-2) Substitute -1 for m and ( 2,-4) for (x1,y1). Simplify Example 3: Using Point-Slope Form Write an equation of the line through point P(3,-6) with slope -8. y-y1=m(x-x1) Use point-slope form Y-(-6)=-8(x-3) Y+6=-8(x-3) Substitute -8 for m and ( 3,-6) for (x1,y1). Simplify

Writing an Equation of a Line Given Two Points 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. Step 2: Select one of the points. Write an equation in point-slope form. y2-y1 m= x2-x1 y-y1=m(x-x1) -1-3 m= Y-3=(-4/3)[x-(-2)] Y-3=(-4/3)(x+2) 1-(-2) -4 m= 3

Writing an Equation of a Line Given Two Points 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. Step 2: Select one of the points. Write an equation in point-slope form. y2-y1 m= x2-x1 y-y1=m(x-x1) 1-(-9) m= Y-(-9)=(-2)(x-4) Y+9=(-2)(x-4) -1-4 10 m= -5 y-y2=m(x-x2) m= -2 Y-1=(-2)(x-(-1)) Y-1=(-2)(x+1)

Equations of Horizontal and Vertical Lines 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. 2 4 6 -2 -4 -6 P(3,2)

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