Lesson 5.5 Writing Equations in Point-Slope Form
pages 286-291
Vocabulary:
point-slope form-an equation of the form
y-y=m(x-x ) ,where m is the slope and
(x , y ) is a given point on a non vertical
line.
1
1
1
1
Example 1 Write an equation given slope and a point
Write the point-slope form of an equation for a line that
passes through (3, -2) with a slope 2/3
Step 1 Point Slope Form
Step 2 Substitution
Step 3 Simplify
y-y1=m(x-x1)
y- (-2)=2/3 (x-3)
y + 2 = 2/3(x-3)
This is your answer because it is in point-slope form.
Example 2 Write an Equation of a Horizontal Line
Write the point-slope form of an equation for a line that passes
through (1/2,1) and is horizontal.
Slope =0
Step 1 Point Slope Form
Step 2 Substitution
Step 3 Simplify
y-y1=m(x-x1)
y-1=0(x-1/2)
y-1=0
Step 4 Additive Inverse
+1
+1
Step 5 Simplify
y=1
Example 3 Write an Equation in Standard Form
Write y - 4=1.6 (x+2)
Step 1 Original Equation
in Standard Form Ax+By=C
y-4=1.6(x+2)
Step 2 Multiply each side by 5 eliminate the decimal
5 (y-4)=(1.6)(5)(x+2)
Step 3 Distributive Property
5y-20=8(x+2)
Step 4 Distributive Property
5y-20=8x+16
Step 5 Simplify, Additive Inverse
-8x
+20
5y=8x+36
Step 6 Simplify, Subtract 8x from each side
Step 7 Simplify and arrange
+20
HINT:
You want to get x and y
on one side and
constant on another
-8x
-8x + 5y =36
Example 4 Write an Equation in Slope-Intercept Form
Write y + 1 = -3 (x+3)
in Slope-Intercept Form
y=mx + b
Step 1 Original Equation
y + 1 = -3(x + 3)
Step 2 Distributive Property
y + 1 = -3x -9
Step 3 Subtract 1 from each side
-1
y=-3x - 10
Step 4 Simplify
Make sure it is in
y=mx + b
-1
Example 5 Write an Equation in Point-Slope Form
The figure shows right triangle ABC.
A. Write the point-slope form of the line containing the
hypotenuse AB.
B (6,4)
Step 1 First, find the slope of AB.
A
(2, 1)
Step 2 You can use either point for (x1,y1)
in the point-slope form.
Method 1 Use (6,4)
y-y1=m(x-x1)
Method 2 Use (2,1)
y-y1=m(x-x1)
B. Write each equation in standard form . Ax+By=C
C
(6,1)