Linear vs. Exponential Patterns

Front

What is a linear pattern?

Back

A linear pattern is a relationship between two variables that can be represented by a straight line on a graph. It follows the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential pattern?

Back

An exponential pattern is a relationship where a quantity increases or decreases at a constant percentage rate over time. It can be represented by the equation y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

How do you identify a linear relationship from a table of values?

Back

A linear relationship can be identified if the differences between consecutive y-values are constant as x increases.

Front

How do you identify an exponential relationship from a table of values?

Back

An exponential relationship can be identified if the ratios of consecutive y-values are constant as x increases.

Front

What is the slope in a linear equation?

Back

The slope (m) in a linear equation represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) in a linear equation is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = ab^x, where a is the initial value, b is the growth (b > 1) or decay (0 < b < 1) factor, and x is the exponent.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

How can you graph a linear equation?

Back

To graph a linear equation, plot the y-intercept on the y-axis, use the slope to find another point, and draw a straight line through the points.

Front

How can you graph an exponential equation?

Back

To graph an exponential equation, plot the initial value (when x=0), calculate additional points using the equation, and draw a smooth curve through the points.