Calculating Slope of a Line

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

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

How do you determine if a slope is positive, negative, or undefined from a graph?

Back

A slope is positive if the line rises from left to right, negative if it falls from left to right, and undefined if the line is vertical.

Front

If a line has a slope of 2, what does this mean in terms of rise over run?

Back

A slope of 2 means that for every 1 unit you move to the right (run), the line rises 2 units (rise).

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

If a line has a slope of -1, what does this indicate about the line's steepness?

Back

A slope of -1 indicates that the line descends at a 45-degree angle 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 unit, or any other relationship between two variables.