1. Writing Linear Equations
Infinity HS
Ms. Sophia Papaefthimiou

2. Linear Equation Examples: 3x + 2y = 5 A = 3, B = 2 and C = 5 x = -6
C is called the constant Ax and By are variable terms.
The equation of a line is often written in the form Ax + By = C
This is called standard form
A ≥ 0
A and B are not both zero
A, B, and C are integers whose greatest common factor is 1
Examples:
3x + 2y = 5
A = 3, B = 2 and C = 5
x = -6
A = 1, B = 0 and C = -6

3. Identify Linear Equations
Directions: Determine whether each equation is linear. If yes, write the equation in standard form.
Ex1: y = 5 – 2x
2x + y = 5
The equation is in standard form where A = 2, B =1, and C = 5. Yes, this is a linear equation.
First rewrite the equation so both variables are on the same side of the equation (Standard Form: Ax + By = C)

4. Identify Linear Equations (cont’d)
Ex2: 2xy – 5y = 6
Since the term 2xy has two variables, the equation cannot be written in the form Ax + By = C. Therefore, this is not a linear equation.
Ex3: y = x2 – 4
Since the term x2 is squared, the equation cannot be written in the form Ax + By = C.
Therefore, this is not a linear equation.

5. Identify Linear Equations (cont’d) (HW Prob #4)
Ex4:
The equation is in standard form where A = 2, B =-1, and C = 6. Yes, this is a linear equation.
To write the equation with integer coefficients, multiply each term by 3.

6. Identify Linear Equations (cont’d)
Ex5:
The equation is in standard form where A = 3, B = -4, and C = 60. Yes, this is a linear equation.
Subtract 2y/3 from both sides
Multiply each term on both sides by 6
Simplify
Answer: 3x – 4y = 60

7. Linear or Non-linear Function
For a function to be linear, the rate of change must be constant, meaning the change in the y-values must be constant and the change in the x-values must be constant.
Ex1: Does the table below show a linear relationship? x y 1 2 3 4 6
Yes, the rate of change is constant (the change in the y is constant, the change in the x is constant.) Thus, the function is linear.

8. Linear or Non-linear Function (cont’d)
Ex2: Does the table below show a linear relationship? x y 1 6 2 12 3 18 4 24
Yes, the rate of change is constant (the change in the y is constant, the change in the x is constant.) Thus, the function is linear.

9. Linear or Non-linear Function (cont’d)
Ex3: Does the table below show a linear relationship? x y 12 -4 9 1 6 3 11 16
Yes, the rate of change is constant (the change in the y is constant, the change in the x is constant.) Thus, the function is linear.

10. Linear or Non-linear Function (cont’d)
Ex4: Does the table below show a linear relationship? x y -3 10 -1 12 1 16 3 18 5 22
No, this rate of change is not constant. Thus, the function is not linear.

11. HW#2 Answers Yes, x – y = -5 Yes, 2x + y = -3 Yes, -4y = -4

12. Warm-Up
Write the following equations in standard form, Ax + By = C
1. x = y – 8 2.
3. 3x + 9y = 15 (Hint: The GCF of 3, 9, and 15 is not 1)
x – y = -8 (subtract y from both sides)
y = -3 (multiply each side by 3)
x + 3y = 5 (divide all the terms by 3, so that the GCF is 1)