Download Connecting Variation, Slope, and First Differences

MPM1DI
Connecting Variation, Slope, and First Differences
A relation can be expressed in four ways (the text refers to this as the rule of four):
 using words (the description of the situation)
 using numbers (a table of values)
 using a diagram or graph
 using an equation
Recall that the equations of a line has the form y = mx + b, where m represents the slope and b represents the
vertical intercept.
Example 1: Consider two points A(x1, y1) and B(x2, y2). Calculate the slope of line segment AB.
Example 2:
Given A(-2, 13) and B(4, 5), calculate the slope of the line segment AB.
Example 3:
Determine the slope of the following using 2 different methods.
x
y
-4
-10
-1
-5
2
0
5
5
8
10
MPM1DI
Connecting Variation, Slope, and First Differences
Example 4: a) For the following relation described in words, express the relation in 3 other ways (table,
graph, and equation)
Words: A house painter charges $400 plus $200 per room to paint the interior of a house.
b) Describe what the slope means.
c) How can you identify from each of the 4 forms if a relationship demonstrates direct or partial variation?
Example 5:
a) Calculate the slope using 2 methods.
b) Determine the vertical intercept.
c) Write an equation for the relation.
Homework: Pg. 284: #1, 2, 3a, 5 - 10, 13