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MATHEMATICS OBJECTIVE
Students will be able to:
Find the slope of a line using different strategies.
Interpret a slope in context and relate it to steepness on a graph.
ESSENTIAL UNDERSTANDING
Slope is a measure of the steepness of a line and is equal to the rate of
change between quantities. In a proportional relationship, the slope is the same as the unit rate and the constant of proportionality.
I can find and describe slopes of proportional relationships.
SLOPE
Slope is the measure of the steepness of a line. It represents the ratio of
the rise (that is, the vertical distance) to the run (the horizontal distance)
between two points on the line. In proportional relationships, slope is the
same as the unit rate and constant of proportionality.
slope = rise / run
= (change in y-coordinates) / (change in x-coordinates)
= (y2 - y1) / (x2 - x1)
GRAPH: THEATER PRICE
x-axis: Number of Tickets
y-axis: Cost ($)
The graph is a straight line through the origin.
Labeled points include (1, 15), (3, 45), and (5, 75).
The diagram highlights the points (3, 45) and (5, 75):
rise = 75 - 45 = 30
run = 5 - 3 = 2
rise / run = 30 / 2 = 15
The slope of the line is 15.
1 ticket costs $15. The constant of proportionality is 15.
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