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Foundations & Pre-Calculus 10
6.2 Linear Relations
Recall that a relation is an association between two quantities. A linear relation will have a
graph that is a line. A non-linear relation will have a graph that is some type of curve. To
determine if a relation is linear from a table of values, check to see how the x and y values are related. If the x and y values increase or decrease by a constant amount, then the data would be for a linear relation (except for horizontal or vertical lines). Non-linear relations would have x and y values that increase or decrease by different amounts.
Example:
Linear Relation Non-Linear Relation
Equation: Equation:
x y
x y
Graphs of linear relations may contain one of two different types of data:
Discrete Data:
Continuous Data:
For what type of situation would you see each type of data?
In relations that contain two variables, one variable is considered to be independent while
the other is considered to be dependent. As would be expected, the dependent variable‟s
values depend on the values of the independent variable.
- When data is presented in tabular form, the ________________ values are found in the first column and the _________________ values are found in the second column.
- When data is presented in graph form, the _________________ values are on the x-axis (horizontal) and the ________________ values are on the y-axis (vertical).
c) The relation described by the following equation: g + 4 = 0.7h
- Allie has collected some data on students‟ heights as they age. Which category would be the dependent variable? Which would be the independent variable?
6.3 Warm-Up
1. Describe in words the values represented by the number line. 2. Draw a number line to represent all numbers that are less than – 2. 3. Describe in words the values represented by the number line. 4. Draw a number line that represents all numbers that are greater than 4 and less than or equal to 7. 5. A car travels at 60 km/h for 5 h. Suppose you were to create a graph of this scenario. a) What scale would you use along the time axis? What value would you start at? What value would you end at?
b) What scale would you use along the distance axis? What value would you start at? What value would you end at?
