Find: Rise Over Run

Front

What is the definition of slope in mathematics?

Back

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

Front

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

Back

The slope (m) can be 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 does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

What is the slope of a horizontal line?

Back

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

Front

If a line has a slope of -3, what does this mean in terms of rise and run?

Back

A slope of -3 means that for every 1 unit increase in the run (horizontal change), the rise (vertical change) decreases by 3 units.

Front

What is the slope of the line represented by the equation y = 2x + 5?

Back

The slope of the line is 2, which is the coefficient of x in the slope-intercept form of the equation (y = mx + b).

Front

How can you determine the slope from a graph?

Back

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

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope, meaning they will never intersect and have identical steepness.