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 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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

How do you determine the slope from a graph?

Back

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

Front

If a line has a slope of 2, what does this mean in terms of rise and 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 (3, 7) and (3, 10)?

Back

The slope is undefined because the line is vertical.

Front

If a line passes through the points (1, 2) and (4, 5), what is the slope?

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.

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 understand relationships between variables in various contexts, such as speed, cost, and growth.