Linear vs Exponential Practice

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. The graph of an exponential function increases or decreases rapidly.

Front

How do you identify a linear pattern in a table of values?

Back

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

Front

How do you identify an exponential pattern in a table of values?

Back

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

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the purpose of linear regression?

Back

Linear regression is used to find the best-fitting line through a set of data points, allowing for predictions based on the relationship between variables.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

Front

How do you write the equation of a line given two points?

Back

To write the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m = (y2 - y1) / (x2 - x1)), then use the point-slope form: y - y1 = m(x - x1).