In this Grade 7 lesson from Big Ideas Math Advanced 2, students learn to identify linear and nonlinear functions by analyzing whether the rate of change is constant across tables, graphs, and equations. The lesson covers key skills such as recognizing nonlinear functions like y = 4/x that cannot be written in slope-intercept form, and distinguishing them from linear functions using equal intervals. Real-life applications, including comparing simple and compound interest and falling objects, reinforce how linear and nonlinear patterns appear in everyday contexts.
Section 1
Rate of Change
A rate is a type of ratio that compares two quantities with different units.
A rate of change is a special kind of ratio that compares the change in two quantities or variables.
In mathematics, we use the symbol (delta) for change in. Thus, a rate of change can be expressed as the ratio of the change in one variable to the change in another:
Section 2
Lines Have Constant Slope
The slope of a line is constant: no matter which two points you pick to compute the slope, you will always get the same value.
Because is constant for a given line, we can use the formula to find when we know , or to find when we know .
We can also tell whether a collection of data points lies on a straight line by computing slopes between them.
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Section 1
Rate of Change
A rate is a type of ratio that compares two quantities with different units.
A rate of change is a special kind of ratio that compares the change in two quantities or variables.
In mathematics, we use the symbol (delta) for change in. Thus, a rate of change can be expressed as the ratio of the change in one variable to the change in another:
Section 2
Lines Have Constant Slope
The slope of a line is constant: no matter which two points you pick to compute the slope, you will always get the same value.
Because is constant for a given line, we can use the formula to find when we know , or to find when we know .
We can also tell whether a collection of data points lies on a straight line by computing slopes between them.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter