Title: Algebra 1
Author: Mandy McDaniel
Last saved by: MHE

Lesson 4-5

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 slope .
	y - y = m(x - x)	Point-slope form	
	y – (-2) = (x - 3)	(x_1, y_1) = (3, -2)
	y + 2 = (x - 3)	Simplify.
Therefore, the equation is y + 2 = (x - 3).

Example 2 Write an Equation of a Horizontal Line
Write the point-slope form of an equation 
for a horizontal line that passes through (, 1).
y - y = m(x - x)	Point-slope form	
 y – 1 = 0(x - )	(x_1, y_1) = (, 1)
 y – 1 = 0	Simplify.

Therefore, the equation is y – 1 = 0.

Example 3 Write an Equation in Standard Form
Write y – 4 = 1.6(x + 2) in standard form.
In standard form, the variables are on the left side of the equation. A, B, and C are all integers.
	 y – 4 	= 1.6(x + 2)	Original Equation
	5(y – 4)	= 5(1.6)(x + 2)	Multiply each side by 5 to eliminate the decimal.
	5y – 20 	= 8(x + 2)	Distributive Property
	5y – 20 	= 8x + 16	Distributive Property
  5y – 20 + 20 = 8x + 16 + 20	Add 20 to each side.
	5y 	= 8x +36	Simplify.
	5y – 8x 	= 8x + 36 – 8x	Subtract 8x from each side.
	 -8x + 5y 	= 36	Simplify.

The standard form of the equation is –8x + 5y = 36.

Example 4    Write an Equation in Slope-Intercept Form
Write y + 1 = -3(x + 3) in slope-intercept form.
	y + 1 = -3(x + 3)	Original equation
	y + 1 = -3x – 9	Distributive Property
	y + 1 – 1 = -3x – 9 – 1	Subtract 1 from each side.
		y = -3x – 10	Simplify.
The slope-intercept form of the equation is y = -3x – 10.

Example 5    Write an Equation in Point-Slope Form
GEOMETRY  The figure shows rectangle DEFG.		
a.	Write the point-slope form of the line containing the
diagonal  of the rectangle.
Step 1	First, find the slope of .
m = 	Slope formula
	=  or -	(x_1, y_1) = (-1, 2), (x_2, y_2) = (-4, 4)

Step 2	You can use either point for (x, y) in the point-slope form.
Method 1 Use (-1, 2)		Method 2 Use (-4, 4)
y - y = m(x - x)		y - y = m(x - x)
y - 2 = -(x – (-1))		y - 4 = -(x – (-4))
y - 2 = -(x + 1)		y - 4 = -(x + 4)

b.	Write each equation in standard form.
 y - 2	= -(x + 1)	Original equation	y - 4 = -(x + 4)
3(y – 2)	= 3 (x + 1)	Multiply each side by 3.		3(y – 4) = 3 (x + 4)
  3y – 6 	= -2(x + 1)	Multiply.	3y – 12 = -2(x + 4)
3y – 6 	= -2x – 2	Distributive Property	3y – 12 = -2x – 8
 3y 	= -2x + 4	Add to each side.	3y = -2x + 4
2x + 3y = 4	Add 2x to each side	2x + 3y = 4