GOAL: To further understand the use of slope
We know the x-axis and y-axis are perpendicular to each other.
If we rotate each axis by 45 degrees we will get the lines y=x and y=-x, which will still be perpendicular to each other.
Recall that the slope of y=x is 1.
Recall that the slope of y=-x is -1.
What is the relationship between these two lines and their respective slopes?
Let's look at two other perpendicular lines:
The line through the points (0,0) and (2,1) will be perpendicular to the line through (0,0) and (-1,2)
What are the equations of these lines? y=(1/2)x and y=-2x
What are the slopes of these lines? m=(1/2) and m=-2
What is the relationship between the slope of these two lines? They are negative reciprocals of each other.
CONJECTURE: The slopes of two perpendicular lines will be negative reciprocals of each other.
Graph lines that are perpindicular and see whether this relationship holds true.
The lines graphed above are y=x and y=x+1.
These two lines are parallel since they do not intersect.
What are the slopes of these two lines? They are the same.
Will this hold true for all parallel lines? Yes.
What will the distance between these two lines be at any point x? Constant since the lines have the same slope.
EXTENSIONS:
1. Find x so that the line through (3,4) and (x,6) will have slope -(2/5).
2. Find the slope of a line passing through (0,0) and (3,12).
3. Find the slope of the line 2x-6y=40.
4. Find the slope of the line y=-(3/4)x + 5.
5. a)Find the y-intercept of each line shown in the graph below.
b) Describe an efficient way to find the y-intercept from the equation of the line.