Finding Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y (rise) over the change in x (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 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 rise 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 is 0, leading to division by zero.

Front

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

Find the slope of the line passing through the points (2, -3) and (5, 0).

Back

The slope is m = (0 - (-3)) / (5 - 2) = 3 / 3 = 1.

Front

If the slope of a line is -3, what does this tell you about the line?

Back

The line falls steeply from left to right, indicating a negative relationship between x and y.

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.