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LESSON 5: GENERAL FORM OF THE EQUATION FOR A LINEAR
RELATION
Learning Outcome: Learn to relate the graph of a linear function to its
equation in general form.
Work with a partner.
Holly works in a furniture plant. She takes 30 min to assemble a table and
15 min to assemble a chair. Holly works 8h a day, not including meals and
breaks.
A. Complete the table of values for the possible numbers of tables and
chairs that Holly could assemble in one day.
Number of Tables
16
15
Number of Chairs
0
2
B. Graph the data. Use a graphing calculator if available. Describe the
graph. What type of relation have you graphed? How do you know?
C. What do the intercepts represent?
D. Choose variables to represent the number of tables and number of
chairs. Write an equation for your graph.
The equation 2x – 3y = 12 is written in standard form. The coefficients and
constant terms are integers.
The x- and y- terms are on the left side of the equation, and the constant
term is on the right side.
We may move the constant term to the left side of the equation:
2x – 3y – 12 = 0
The equations is now in general form.
Ax + By + C = 0 is the general form of the equation of a line, where A
is a whole number, and B and C are integers.
What happens to the equation in general form when A = 0?
You are left with By + C = 0
𝑦= −
𝐶
𝐵
You are left with a horizontal line.
What happens to the equation in general form when B = 0?
You are left with Ax + C = 0
𝑥= −
𝐶
𝐴
You are left with a vertical line.
Ex. Rewrite the following equations in general form.
2
a. 𝑦 = − 𝑥 + 6
3
b. 𝑦 + 2 =
3
2
(𝑥 − 4)
Ex. For the linear equation 2𝑥 − 3𝑦 − 6 = 0
a) state the x-intercept of the graph:
b) State the y-intercept
c. Use the intercepts to graph the line:
Ex. Determine the slope of the line with the an equation of:
5𝑥 − 2𝑦 + 12 = 0
Ex. Akeego is making a ribbon shirt. She has 60cm of ribbon that she will
cut into 5 pieces with 2 different lengths: 2 pieces have the same length
and the remaining 3 pieces also have equal lengths.
a) Generate some data for this relation showing the possible lengths of
the pieces.
Remaining 3
pieces with equal
lengths
2 pieces with
same length
Remember the sum of both columns need to add to 60 cm.
b) Graph the data:
c) Write an equation for the relation in general form:
use points (2, 27) and (6, 21)
d) i) Can each of 2 pieces be 18cm long and each 3 pieces be 3 cm
long? (use the graph to determine answer)
ii) Can each of 2pieces be 3cm long and each of 3 pieces be
18cm long?
Assignment: pg. 384 -385 #4-18, 20-24, 26