Finding Slope

Front

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does it mean if the slope of a line is undefined?

Back

An undefined slope indicates a vertical line, where the change in x (x2 - x1) is zero, leading to division by zero in the slope formula.

Front

How do you determine the slope of a line that passes through the points (6,7) and (4,2)?

Back

Use the slope formula: m = (2 - 7) / (4 - 6) = -5 / -2 = 5/2.

Front

What is the slope of a line that passes through the points (2, 4) and (6, 12)?

Back

The slope is calculated as m = (12 - 4) / (6 - 2) = 8 / 4 = 2.

Front

What is the significance of a positive slope in a linear equation?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

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 y as x changes.

Front

How can you interpret the slope in a real-world context, such as rainfall?

Back

In the context of rainfall, the slope can represent the rate of rainfall over time, such as 2 cm per hour.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the change in x is zero.

Front

How do you find the slope of a line given its equation in slope-intercept form (y = mx + b)?

Back

In the equation y = mx + b, m represents the slope of the line.