4. Find Slope from Two Points

Front

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

Back

The formula for slope is m = (y2 - y1) / (x2 - x1).

Front

How do you find the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the change in x (x2 - x1) is zero, leading to division by zero.

Front

What does a positive slope indicate about the direction of a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that as x increases, y 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 because there is no change in y (y2 - y1 = 0) regardless of the change in x.

Front

Given the points (2, 3) and (4, 7), what is the slope of the line connecting them?

Back

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

Front

If the slope of a line is 3, what does this mean in terms of rise over run?

Back

A slope of 3 means that for every 1 unit you move to the right (run), the line rises 3 units (rise).

Front

How do you determine if two points are on a vertical line?

Back

Two points are on a vertical line if they have the same x-coordinate (e.g., (x, y1) and (x, y2)).

Front

What is the slope between the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

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

Back

The slope can represent rates of change, such as speed, growth, or any relationship where one quantity changes in relation to another.