Slope and Proportional Relationships Review

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the rise (vertical change) to the run (horizontal change) between two points on the line.

Front

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

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

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

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where their ratio is constant.

Front

How can you identify a proportional relationship on a graph?

Back

A proportional relationship on a graph is represented by a straight line that passes through the origin (0,0).

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 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 there is no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the run (change in x) is 0, leading to division by zero.

Front

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.