Slope practice

Front

What is the definition of slope?

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

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is: 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 because the change in x (run) is 0, leading to division by zero.

Front

Calculate the slope of the line passing through the points (2, 3) and (4, 7).

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -3, what does this tell you about the line's direction?

Back

A slope of -3 indicates that the line falls steeply from left to right.

Front

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

Back

The slope of the line 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 = -rac{1}{2}x + 3?

Back

The slope of the line is -rac{1}{2}, indicating that for every 1 unit increase in x, y decreases by rac{1}{2} units.