10.13 Parallel and perpendicular lines in linear functions
In previous chapters from lower grades, we discussed all about Linear Equations and Linear Relations, and we know from here that these equations when plotted in a graph would show a line that could either go up or down diagonally since the values of the ordered pairs show a linear relationship. We learned all about the general form of the linear equation which is Ax + By + C = 0 and the slope intercept form which is the y = mx + b. We also learned that the slope, is basically the rise and run of the equation, and b is the y intercept, which is computed by letting x be equal to zero.
Now in this chapter we will discuss Linear Functions which would basically cover all what we have learned about the Linear Relations and Equations. We will study about the distance formula and the midpoint formula for the first two parts of this chapter. In the next few chapters we will review the basic concepts we have discussed before like the slope formula, the slopeintercept form, the general form and then we would be introduced to the slope point formula. We would also learn about the rate of change, which is not only used in the Linear Functions but also in other math concepts.
This chapter would also discuss applications of graphing linear functions depending on the given values that we are going to be given like solving problems that involve graphing linear functions and the parallel and perpendicular line in linear functions.
In this chapter we will learn that parallel lines have identical slopes, that in able to find the parallel line of a linear function, we would need to use the point slope formula that would be discussed in the early parts of the chapter. Perpendicular lines on the other hand would need the negative reciprocals of the slope to find the line that would be perpendicular to the linear function that we have.
In the last part of the chapter we will get to look at the applications of Linear functions like solving for the average rate of change of population, calculating the cost of production, determining hourly rates and more. There are also free online games that you could try to see how linear functions look like.
Parallel and perpendicular lines in linear functions
Lessons
Notes:
Parallel lines$$identical slope so they never intersect each other, unless overlapped.
Perpendicular lines$$two lines form right angles to each other when they intersect. If the slope of first line is ${a \over b}$, the slope of perpendicular line is the slope of perpendicular line is $ {b \over a}$. The product of the two slopes is 1.

a)
$m_1 = {2 \over 5}, m_2= {2 \over 5}$

b)
$m_1 = {1 \over5} , m_2 =  {5 \over 1}$

c)
$m_1 = {4 \over 7}, m_2 = {12 \over 21}$

d)
$m_1 =$undefined, $m_2 = 0$

e)
$m_1 =mn^{1}; m_2 =m^{1}b$


3.
Given the points of two lines, determine when the lines are parallel, perpendicular or neither.