Slope With Two Points

Front

What is the formula for calculating 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 on a graph?

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 on a graph?

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 does a slope of zero indicate about a line?

Back

A slope of zero indicates that the line is horizontal, meaning there is no change in the y-coordinate as the x-coordinate changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning the x-coordinate does not change as the y-coordinate changes.

Front

How do you determine the slope of a line that passes through the points (a, b) and (c, d)?

Back

Use the slope formula: m = (d - b) / (c - a).

Front

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

Back

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

Front

What is the slope of a line that passes through the points (1, 2) and (1, 5)?

Back

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

Front

If a line has a slope of 3, what is the change in y when x increases by 2?

Back

The change in y would be 3 * 2 = 6.

Front

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

Back

The slope represents the rate of change, which can be used to analyze trends, such as speed, growth, or efficiency.