The Equation of a Line in Standard Form: Ax + By + C = 0

The Equation of a Line in Standard Form: Ax + By + C = 0

The equation of a line can be expressed in different ways:
• Recall the equation of the line in slope yintercept form: y=mx+b
• Standard form: Ax+By+C=0
– A, B, and C are integers (No fractions)
– Both A and B are not equal to 0 (A0 and B0)
– The coefficient of the xterm is always positive

Example 1: Convert, y = -2x + 4 from Slope yintercept form to Standard Form

Solution: y=-2x+4
Y+2x-4=0 Transpose all terms so they are on the left. What happens to a term when you transpose it? (The sign change)
2x+y-4=0 Are all the conditions for Standard form met? (Yes)

Example 2: Rearrange the equation from Standard Form to express it in the form of y=mx+b.

a) x + 5y- 6 = 0
b) 8x-4y-20 = 0
Solution:
a) x + 5y- 6 = 0
Solve for y.
5y=-x+6
5y5=-x+65
y=-x+65
∴y=-x5+65
b) 8x-4y-20 = 0
-4y=-8x+20
-4y-4=-8x+20-4
y=-8x-4+20-4
y=2x-5

Example 3: The Celebrations Banquet Hall uses the equation

15n-C+750=0 to determine the cost for a hall rental, where C represents the cost, in dollars, which depends on n, the number of people attending.
a) Express the equation in slope yintercept form: C = mn + b
15n-C+750=0
15n+750=C
C=15n+750
b) Identify the fixed and variable costs
Fixed cost is $750
Variable cost is 15n
c) What is the rental cost if 150 people attend a soccer banquet?
Sub. n=150
C=15n+750
C=15150+750
=2250+750
=3000
∴ The rental cost would be $3000.00
d) Illustrate the relation graphically.