Slopey Slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

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 you move from left to right along the line, the line rises. This means that the y-value increases as the x-value increases.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as you move from left to right along the line, the line falls. This means that the y-value decreases as the x-value increases.

Front

What is the slope of a horizontal line?

Back

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

Front

If two lines are parallel, what can be said about their slopes?

Back

The slopes of parallel lines are the same.

Front

If two lines are perpendicular, how are their slopes related?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one slope is m, the other slope is -1/m.

Front

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

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (5 - 2) = 4/3.

Front

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

Back

The slope of the line is 2, which is the coefficient of x in the equation.