GOAL: To understand and determine the slope of a line
DEFINITION: The slope of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right.
We represent the slope with the letter m.
The graph shown above is the graph of the line y=x.
This line rises 1 unit for each 1 unit of horizontal change from left to right.
Therefore, this line has a slope of m=1/1, or m=1.
The graph shown above is the graph of the line y=-x.
This line falls 1 unit, or rises -1 unit, for each 1 unit of horizontal change from left to right.
Therefore, this line has a slope of m=-1/1, or m=-1.
NOTE:
POSITIVE SLOPE , LINE RISES
NEGATIVE SLOPE , LINE FALLS
CALCULATION OF SLOPE:
change in y / change in x = Y2-Y1 / X2-X1 ; where (X1,Y1) and (X2,Y2) are points on line.
What is the slope of a horizontal line?
Let's look at the line y=5:
Use Formula:
Choose two points on the line
(0,5) , (1,5)
m= change in y / change in x = Y2-Y1 / X2-X1 = 5-5 / 1-0 = 0 / 1 = 0 = m
The slope of the line y=5 is 0.
What about the slope of any horizontal line?
Since a horizontal line can be written in the form y=b, for any number b, the y-coordinate of any point chosen on the line will be b. Therefore, the numerator in the slope formula will always be b-b = 0. Since 0 divided by anything is 0, the slope of any horizontal line will be 0.
EXTENSION: What is the slope of a vertical line?
HINT: Graph y=nx, where n is the slope of the line and animate.