10.7 Combination of both parallel and perpendicular line 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 10.1.

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 10.2 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 10.3 and 10.4 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 chapter 10.5 and 10.6. 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 10.7 and 10.8 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 10.8. To find out more about linear equations you can check out a video made by Education Alberta in Canada about “Exploring Linear Equations

Combination of both parallel and perpendicular line equations

In this section, we will look at various kinds of questions related to parallel and perpendicular line equations. For instance, we will try to look for the slope of a line that is parallel and perpendicular to a given equation, to figure out if a given pair of line equations is parallel, perpendicular, or neither, and to find the parallel and perpendicular line equations of a given line and a pass through point.


  • 1.
    Find the slope of a line that is parallel and perpendicular to the following.
  • 2.
    Given the equations of the following line determine if they parallel, perpendicular, or neither.
  • 3.
    Find the equation of the line that passes through given point and is i.) parallel ii.) perpendicular to the given line.
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Combination of both parallel and perpendicular line equations

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