8th Grade Math - Proportional Relationships Lesson
Recall that a proportional relationship can be represented by an equation of the form y = kx, where k is a constant.
The constant, k, is referred to as the constant of proportionality, the unit rate, and/or the slope.
Notice in the equation y = kx, if x equals 1, then y equals k.
So, on the graph of a proportional relationship, when x equals 1, the corresponding y-value is the slope.
In the equation y = kx, if x equals 0, then y also equals 0.
So, on a coordinate grid, a line drawn through points which represent a proportional relationship, and extended through the x-axis, contains the point (0, 0).
Also notice, in the equation y = kx, if we divide both sides by x, we get y/x = k.
So, for a given (x, y) in a proportional relationship, the slope is the ratio of y to x, x ≠ 0.
A pound of fudge costs three different prices at three different candy stores. The representations below show the cost, y, based on the number of pounds of candy, x, at the three stores. For each representation, identify and interpret the slope.
For an equation of the form y = kx, k is the slope.
For the given equation, the slope is 16.
In this situation, the slope can be interpreted as $16 per pound of candy.
In the table, the ratio of each y to its corresponding x is 11.
So, the slope of the line represented by the table is 11.
In this situation, the slope can be interpreted as $11 per pound of candy.
The graph represents a proportional relationship.
On the graph of a proportional relationship, when x equals 1, the corresponding y-value is the slope. On this graph, when x equals 1, y equals 8. So, the slope is 8.
The slope can be interpreted as $8 per pound of candy.