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, calculated 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

Slope (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, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

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

Front

If a line has a slope of -3, what does this mean?

Back

This means that for every 1 unit increase in the x-direction, the y-value decreases by 3 units.

Front

Find the slope of the line passing through the points (2, 3) and (5, 7).

Back

Slope = (7 - 3) / (5 - 2) = 4 / 3.

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope is 2, which means for every 1 unit increase in x, y increases by 2 units.

Front

What is the slope of the line represented by the equation y = -1/4x + 3?

Back

The slope is -1/4, indicating that for every 1 unit increase in x, y decreases by 1/4 units.