Find the slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope between 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 a line?

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 a line?

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, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change (run) is 0, leading to division by zero.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, identify two points on the line, calculate the rise (vertical change) and run (horizontal change) between them, and then divide rise by run.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

If a line has a slope of 0, what can be said about its equation?

Back

If a line has a slope of 0, its equation is of the form y = b, where b is a constant, indicating a horizontal line.

Front

What is the slope of the line that passes through the points (1, 2) and (4, 5)?

Back

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