Linear, Proportional, & Slope Review for Flashcard

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness of a line, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio, meaning they increase or decrease together at the same rate.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant, meaning they do not increase or decrease together at the same rate.

Front

How can you identify if a graph represents a proportional relationship?

Back

A graph represents a proportional relationship if it passes through the origin (0,0) and forms a straight line.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

Slope (m) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the slope of the line that passes through the points (2, 4) and (6, 12)?

Back

Slope (m) = (12 - 4) / (6 - 2) = 8 / 4 = 2.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that y does not change as x changes.