This week, we mainly focused on slope and parallel and perpendicular lines.
Slope is the change in y, and the change in x. This can be measured as rise/run. Since rise means to go up, and doing so is on the y-axis, rise=y. Since running means to go to the side, this is on the x-axis.
The formula for slope is rise/run (y/x) or change in y=71-y2/change in x=x1-x2
Here I will bold the x1 and y1 numbers.
(2,9) and (-5, 12)
So this means that (y) =9-12 and (x)= 2–5=-3/7
If we do this with the opposite numbers as x1 and y1, we will get the same answer but in a different form.
(2, 9) and (-5,12), that will mean
(y)=12-9 and (x)=-5-2. This, ultimately will give us the same numbers, but instead it will be 3/-7.
Parallel Lines are lines that have the same slope, but will never cross. A parallel line can have the same slope, but based on the starting point, it will never cross with the other line.
Rule:For a parallel line, m1=m2, which also proves that the slope is the same. The length of the lines do not have to be the same length.
Perpendicular Lines are lines that have the slope as recipricals of eachother, and will eventually cross at a right angle. These kinds of line segments do not have the same slope, and as a result, the lines will cross.
Rule: For a perpendicular line, as long as the answer of m1-m2 or any other combonation is equal to -1, it is a perpendicular line.
