12.1 Introduction to linear equations
We have learned all about linear relationships, and linear functions. From what we learned about, we know that linear relationships and functions is consisted of two variables, one dependent, and the other independent. We also know that the line is a straight line. Linear equations are nonetheless the same, adding the criteria that its variables should not be raised to an exponent greater than one, and that the variables are not used as a denominator. We are to learn more of linear equations in this chapter, especially in section 1.
Apart from linear equations, we also need to learn about nonlinear equations. As the word suggests, these are the other equations that aren’t linear in nature, like the quadratic equations, circle equations, cubic equations, and more. We will have exercises in section 2 that will show us the difference between these equations and that of the linear equations.
As we have learned in the previous chapters, we know that linear equations show a straight line, that would appear to fall diagonally to on the Cartesian plane, to show the linear relationship between the values found in the line. However, in some special cases, linear equations can show horizontal lines and vertical lines. In chapter section 3 and 4 we will understand these special cases a bit more.
We are also going to learn how to find the parallel line and the perpendicular line of a given linear equation in section 5 and section 6. From our previous discussion in chapter, we learned that parallel lines have the same slope, whereas perpendicular lines have the slopes that are negative reciprocals with each other.
In section 7 and section 8 we have more practice in looking for the parallel lines and perpendicular lines, by looking for both of them for every equation given. There are also other applications of linear equation in section 8. To find out more about linear equations you can check out a video made by Education Alberta in Canada about “Exploring Linear Equations”
Introduction to linear equations
Lessons
Notes:
Expression: A collection of numbers, variables, and signs, such as $3, 3x+4, 5 x^2 + 2, \sqrt{x3},$etc
Equations: A mathematical statement with an equal sign, such as $y = 2, y = 3x2, y = x, x = 3,$etc
Linear Equation: Ax + By = C (A, B & C are constants; x & y are variables)
All linear equations are functions expect a vertical line such as x = 3.

2.
Graph the linear equations: