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

What does a positive slope indicate about the direction of a line on a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, 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-values increase, the y-values decrease, 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

If a line has a slope of 3/2, what does this mean in terms of rise over run?

Back

It means that for every 2 units you move horizontally (run), the line rises 3 units (rise).

Front

How do you determine the slope from a graph?

Back

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

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 growth rates in various contexts.

Front

How can you identify a line with a slope of -1 on a graph?

Back

A line with a slope of -1 will decrease one unit vertically for every one unit it moves horizontally to the right.

Front

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Back

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