1. Compare the following two sentences:
“The Beatles wrote several big hits.”
“A number of big hits were written by The Beatles.”

2. The two sentences basically mean the same thing
The two sentences basically mean the same thing! They are just written differently.
In math, you can also express values and equations that mean the same thing in different ways.
For example:
0.50
50%

3. 6.2 The Equation of a Line in Standard Form Ax + By + C = 0
This is simply another way to write the equation of a straight line

4. Why might we want to change the equation of a straight line from standard form to slope y-intercept form?

5. Changing from Standard Form to Slope y-intercept Form
Isolate the y-term on one side of the equation
x + y - 3 = 0
To do this, isolate y on one side of the equation.
y = - x + 3
What is the slope and y-intercept of this equation?
m = -1, b = 3

6. Example #1
Rearrange the equation from Standard Form to express it in the form of y = mx + b
x + 2y - 4 = 0
2y = -x +4
and b = 2

7. Rearrange the equation from Standard Form to the form y = mx + b
Example #2
Rearrange the equation from Standard Form to the form y = mx + b
6x - 3y – 15 = 0
-3y = -6x + 15
The slope is 2 and the y-intercept is -5

8. Example #3 Express the equation in slope y-intercept form: C = mn + b
The Celebrations Banquet Hall uses the equation n - C = 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.
Express the equation in slope y-intercept form: C = mn + b
Identify the fixed and variable costs
What is the rental cost if 100 people attend a soccer banquet?

9. Solution Slope y-intercept form: 25n - C + 1250 = 0 -C = -25n - 1250
This is a partial variation. The fixed cost is $1250. The variable cost is $25 per person attending.

10. To find the cost for 100 attendees, substitute n = 100 into the equation.
Therefore, it would cost $3750 to rent the banquet ball for 100 people.

11. -3x + 4y – 7 = 0 is not in standard form
Note
For an equation to be in standard form, the coefficient of the x-term must be positive. If it is negative, divide both sides by -1 to express the equation in standard form.
-3x + 4y – 7 = 0 is not in standard form
Thus, let’s multiply EACH side of the equation by -1 to express in standard form:
(-1) (-3x + 4y – 7) = (-1) (0)
3x – 4y + 7 = 0

12. The equation of a straight line can be Expressed in different ways:
Recap of
key points
The equation of a straight line can be
Expressed in different ways:
standard form: Ax + By + C = 0
slope y-intercept form: y = mx + b
You can convert an equation in standard
form to slope y-intercept form by rearranging
the equation.
When in standard form, A and B cannot both
be zero! (One of them can be zero)