FCP 10
6.6 General Form of a Linear Equation
Now that we have looked at slope-point and slope-intercept form we can now look at the
last form. This form is called general form.
The following are examples of linear equations in general form.
3x + 4y + 10 = 0
7x – 4y -9 = 0
What do you notice about the above equations?
10x + 3y - 9 = 0
The general form is when one
side of the equation equals 0.
Ax + By + C = 0
How could you convert an equation from slope intercept form to General Form?
Example 1
Convert the following into general form. (Slope-intercept form  general form)
Convert the following into general form. (Slope-Point form  general form)
y 1
3
( x 2)
5
Example 2
Complete the table for the listed values of x and y
and graph the line made by the equation
x + 2y – 6 = 0
x
y
0
0
2
What is the x-intercept?
What is the y-intercept?
Example 3
Determine the slope of the line with this equation: 3x 2 y 16 0
In order to find the slope from general form we can simply solve for _____
Example 4
Sometimes it’s easier to sketch a graph using its intercepts:
Find the x- and y-intercepts for:
2x – 3y + 6 = 0
Example 5
Peanuts cost $2 per 100g and raisins cost $1 per 100g. Devon has $10 to purchase both
these items.
a) Generate some data for this relation by creating a table of values (t-chart). Then
graph the data.
b) Write an equation for the relation in general form.
d) i) Will Devon spend exactly $10 if she buys 300g of peanuts and 400g of raisins?
ii) Will Devon spend exactly $10 if she buys 400g of peanuts and 300g of raisins?
_________ form is the last form of a linear equation. This form is very close to
general form, with only one major difference.
General Form
Standard form