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

If a line has a slope of 0, what does this indicate about the line's orientation?

Back

A slope of 0 indicates that the line is horizontal.

Front

What does a positive slope indicate about the relationship between the x and y coordinates of a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases.

Front

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

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases.

Front

How do you determine which of two lines is steeper based on their slopes?

Back

The line with the greater absolute value of the slope is steeper.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

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

Front

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

Back

In the equation y = mx + b, m represents the slope of the 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 decline in various contexts.