Slope Formula

Front

What is the slope formula?

Back

The slope formula is given by m = (y2 - y1) / (x2 - x1), where m is the slope, (x1, y1) and (x2, y2) are two points on a line.

Front

How do you interpret a positive slope?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship between the two variables.

Front

What does a negative slope represent?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship between the two variables.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope occurs when a line is vertical, meaning that the x-value does not change while the y-value does.

Front

How can you find the slope between two points (3, 4) and (7, 10)?

Back

Using the slope formula: m = (10 - 4) / (7 - 3) = 6 / 4 = 1.5.

Front

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

Back

The slope can represent rates of change, such as speed, growth rates, or any relationship where one quantity changes in relation to another.

Front

How do you calculate the slope from a graph?

Back

To calculate the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and use the formula m = rise/run.

Front

What is the slope of a line that goes through the points (2, 3) and (2, 5)?

Back

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

Front

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

Back

A slope of -3 indicates a steep line that descends from left to right, with a steepness of 3 units down for every 1 unit across.