Finding Slope From Two Points

Front

What is the formula to calculate the slope between two points?

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate 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, as there is no change in the y-coordinate regardless of the change in the x-coordinate.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in the x-coordinate is 0, leading to division by zero in the slope formula.

Front

How do you find the slope from two points (2, 4) and (6, 12)?

Back

Using the slope formula: m = (12 - 4) / (6 - 2) = 8 / 4 = 2.

Front

If the slope of a line is -2, what does this tell you about the line's direction?

Back

A slope of -2 indicates that for every 1 unit increase in x, the y value decreases by 2 units, meaning the line falls steeply from left to right.

Front

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

Back

The slope represents the rate of change between two variables, which can be used in various contexts such as speed, cost, and growth rates.

Front

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

Back

Two lines are parallel if they have the same slope.

Front

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

Back

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