Proportional Relationships and Slope. Proportional Relationships. A proportional relationship between two quantities is one in which the two quantities vary directly with one another.
Proportional Relationships and Slope
A proportional relationship between two quantities is one in which the two quantities vary directly with one another.
Example: If one item is doubled, the other, related item is also doubled. The equations of direct variation relationships are always in the form y=mx.
On the previous slide, the equation y=mx referred to a direct variation equation.
In this equation, m is the slope of the line and it is also called the unit rate, the rate of change, or the constant of proportionality of the function.
2. Five Gala apples cost $2.00
1. Create a table relating the number of apples to their cost.
2. Graph the information from the table.
3. Create the equation using the table and the graph.
3. Tess riders her bike at 12 mph.
1. Create a table relating number of hours riding and distance travelled.
2. Create a graph using the table.
3. Create an equation using the graph and the table.
Slope describes the steepness of a line.
It is also referred to as the rate of change or the unit rate.
Can also be referred to as rise over run when looking at a graph.
Zero Slope – A horizontal line has a slope of zero
Undefined Slope – A vertical line has an undefined slope
Negative Slope – A line that falls from left to right has a negative slope
Positive Slope – A line that rises from left to right has a positive slope