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

2. 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

3. 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

4. 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

5. 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)

6. 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)

7. Homework
Page
#17-32; 39-44; 47; 52