Finding Slope from Two Points

Front

What is the formula for calculating the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

Given the points (3, 4) and (5, 8), what is the slope?

Back

The slope is 2. Using the formula: m = (8 - 4) / (5 - 3) = 4 / 2 = 2.

Front

What does a positive slope indicate about the relationship between two points?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, showing a direct relationship.

Front

What does a negative slope indicate about the relationship between two points?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, showing an inverse relationship.

Front

If the slope is zero, what does this tell us about the line?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the y-coordinate as the x-coordinate changes.

Front

If the slope is undefined, what does this tell us about the line?

Back

An undefined slope indicates a vertical line, meaning the x-coordinate does not change while the y-coordinate changes.

Front

How do you find the slope between the points (-1, 7) and (2, 2)?

Back

Using the formula: m = (2 - 7) / (2 - (-1)) = -5 / 3.

Front

What is the slope of the line that passes through the points (-2, -3) and (2, 3)?

Back

The slope is 3/2, calculated as m = (3 - (-3)) / (2 - (-2)) = 6 / 4 = 3/2.

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change, which can be used to analyze trends, such as speed, growth, or decline in various contexts.

Front

How can you determine if two points create a steep slope or a gentle slope?

Back

A steep slope has a larger absolute value of the slope (greater than 1), while a gentle slope has a smaller absolute value (less than 1).