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 the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

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

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 on a line?

Back

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

Front

What is the slope of a vertical line?

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because the change in y (y2 - y1) is zero.

Front

How do you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How do you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

Given the points (3, 4) and (7, 10), what is the slope of the line connecting them?

Back

The slope is m = (10 - 4) / (7 - 3) = 6 / 4 = 3/2.

Front

If the slope of a line is -3, what does this tell you about the line's steepness and direction?

Back

A slope of -3 indicates a steep line that descends from left to right.

Front

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

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates.