Lesson 5 – General Form of the Equation for a
Linear Relation
Specific Outcome: 6.1 – Express a linear relation in different forms, and compare the graphs. 6.2 –
Rewrite a linear relation in slope-intercept or general form. 6.3 – Generalize and explain strategies for
graphing a linear relation in general form. 6.4 – Graph, with and without technology, a linear relation given
in general form, and explain the strategy used to create the graph. 6.5 – Identify equivalent linear
relations from a set of linear relations. 7.5 – Graph linear data generated from a context, and write the
equation of the resulting line. 7.6 – Solve a problem, using the equation of a linear relation.
General Form:
Get zero on
one side
𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0
Where A is a whole number and B and C are integers.
I = { …, -3, -2, -1, 0, 1, 2, 3, …}
W = {0, 1, 2, 3, …}
Note: Coefficient in front of the 𝑥 variable must be positive.
Example 1: Write each equation in general form.
a) 𝑦 = 3𝑥 − 4
3
d) 2𝑦 = − 4 𝑥 + 3
g) 𝑦 + 3 =
2
(𝑥 − 5)
3
2
b) 𝑦 = − 3 𝑥 + 4
c) 2𝑦 = −5𝑥 + 9
e) 𝑦 − 1 = −2(𝑥 + 6)
f) 𝑦 + 6 = 5(𝑥 − 10)
1
h) 𝑦 − 2 = −4(𝑥 + 2)
Example 2: Graph the following equations using intercepts.
a) Line 1: 𝑥 + 3𝑦 + 9 = 0
b) Line 2: 2𝑥 − 3𝑦 + 12 = 0
c) Line 3: 4𝑥 − 4𝑦 − 32 = 0
Example 3: Rewrite the following equations in slope-intercept form.
a) 4𝑥 + 2𝑦 − 10 = 0
b) 3𝑥 − 4𝑦 + 12 = 0
c) 2𝑥 + 5𝑦 + 10 = 0
Example 4: The slope of the line with equation 6𝑥 + 5𝑦 − 1 = 0 is
a) −
b) −
6
5
5
6
6
c) 5
1
d) 5
Example 5: Determine the equation, in slope-intercept form, of a line passing through
(5,-5) and is parallel to 3𝑥 − 6𝑦 + 18 = 0.
Example 6: Write the equation of the line, in general form that is perpendicular to
4𝑥 + 4𝑦 + 24 = 0 and has an x-intercept of 8.
Example 7: Write the equation of the line in general form that is parallel to 2𝑥 − 3𝑦 +
7 = 0 and has the same y-intercept as 5𝑥 − 3𝑦 − 12 = 0.
Practice Questions: Page 384 # 5 – 6 (a, c’s), 21, 22, 8, 9(a, b), 12, 14(a, b), 18