1
College Algebra MT 150
Day #1: Section 3.2 – Linear Equations in Two Variables
Today, we want to accomplish five different things:
1. Be able to define a linear equation in two variables
2. Be able to recognize the standard form of a linear equation.
Standard Form: ____________________________
Where, a, b, and c are constants and a & b are not both zero.
3. Be able to explain the “geometric” meaning of the x and y intercepts of a
linear.
a. Intercepts are points where a graph will cross an axis.
b. The x-intercept is the point where the graph crosses the x-axis.
c. The y-intercept is the point where the graph crosses the y-axis.
4. Be able to determine algebraically the x and y intercepts of a line.
a. To determine the x-intercept, replace the ‘y’ in the linear equation
with a zero and then solve for x.
b. To determine the y-intercept, replace the ‘x’ in the linear equation
with a zero and then solve for y.
5. Be able to recognize the forms of equations that correspond to
horizontal and vertical lines.
a. Horizontal: The linear equation for a horizontal line will NEVER
have an x-variable.
b. Vertical: The linear equation for a vertical line will NEVER have a
y-variable.
Examples: (from page 194 in textbook, selected problems: odd’s 1 thru 23)
Instructions: Determine if the following are linear equations or not.
Remember, to be linear, there must be:
a. No exponents on the variables.
b. No division by the variables.
c. No multiplication of the variables
1. 3x + 2(x – 4y) = 2x – y
3. 9𝑥 2 − (𝑥 + 1)2 = 𝑦 − 3
2
6
5
5. 8 – 4xy = x – 2y
7.
9. 2y – (x + y) = y + 2
11. 𝑥 2 − (𝑥 − 1)2 = 𝑦
13. x(y + 1) = 16 – y( 1 – x)
19. x – 1 =
18. 𝑦 2 − 3𝑦 = (1 + 𝑦)2 − 2𝑥
20. 3x – 4 = 89(x – y) – y
Determine the x and y intercepts.
25. 4x – 3y = 12
29. 3y = 9 (graph result)
𝑥
− =2
𝑦
2𝑦
𝑥
−𝑥
27. 5 – y = 10x
39. 3(x + y) + 1 = x – 5 (graph result)
3
Homework assignment (please complete on a separate sheet of paper):
Textbook: p. 194 (2-24 even)
Instructions: Determine if the following are linear equations or not.
2. 9x + 4(y – x) = 3
4. 3x + xy = 2y
6.
𝑥−𝑦
2
+
7𝑦
3
=5
10. (3 − 𝑦)2 − 𝑦 2 = 𝑥 + 2
14.
𝑥−3
2
=
4+𝑦
5
8. 3x – 3(x – 2y) = y + 1
12. (𝑥 + 𝑦)2 − (𝑥 − 𝑦)2 = 1
16. x – 3 =
4𝑥 + 17
5
18. 𝑦 2 − 3𝑦 = (1 + 𝑦)2 − 2𝑥
20. 3x – 4 = 89(x – y) – y
22. 𝑥 2 − 2𝑥 = 3 − 𝑥 2 + 𝑦
24. 16x = y(4 + (x – 3)) – xy
Textbook: p. 195 (30-38 even)
Instructions: Determine the x and y intercepts.
30. 2x – (x + y) = x + 1
32. y – x = x – y (graph this problem)
34. 2x – 3 = 1 – 4y (graph this problem)
36. 4 – 2y = -2 – 6x
38. 3y + x = 2x + 3y + 4