Find: Rise Over Run

Front

What is the definition of slope in mathematics?

Back

The slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line. It is calculated as the ratio of the rise (change in y) to the run (change in x).

Front

How do you calculate the slope between 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 the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero (change in x is 0).

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, find the rise (vertical change) and run (horizontal change) between them, and calculate the slope using the formula m = rise/run.

Front

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

Back

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

Front

What is the significance of the y-intercept 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

How do you interpret a slope of 0 in a real-world context?

Back

A slope of 0 indicates that there is no change in the dependent variable as the independent variable changes, often representing a constant value.