Module 2 Topic 1

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you calculate the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a function to increase over its entire domain?

Back

A function increases over its entire domain if, for any two points x1 and x2 in the domain where x1 < x2, the function value at x1 is less than the function value at x2 (f(x1) < f(x2)).

Front

What are first differences in a table of values?

Back

First differences are the differences between consecutive y-values in a table of values, used to determine if the relationship is linear or non-linear.

Front

How do you determine if a relationship is linear based on first differences?

Back

If the first differences are constant, the relationship is linear. If the first differences vary, the relationship is non-linear.

Front

What is the average rate of change between two points?

Back

The average rate of change between two points (x1, y1) and (x2, y2) is calculated as (y2 - y1) / (x2 - x1).

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables; a positive slope means the line rises, while a negative slope means it falls.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, characterized by a constant rate of change (slope).

Front

What is the difference between a linear and a non-linear function?

Back

A linear function has a constant slope and forms a straight line, while a non-linear function has a variable slope and forms a curve.

Front

How can you identify key features of a graph?

Back

Key features of a graph include intercepts, slope, increasing/decreasing behavior, and any asymptotes or discontinuities.