Introduction to slope

Front

What is the definition of slope?

Back

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

Front

How is slope calculated between two points (x1, y1) and (x2, y2)?

Back

Slope (m) is calculated using the formula: m = \frac{y2 - y1}{x2 - x1}.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, 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-value increases, the y-value 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, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero in the slope formula.

Front

Find the slope of the line passing through the points (2, 3) and (6, 7).

Back

The slope is \frac{7 - 3}{6 - 2} = \frac{4}{4} = 1.

Front

Find the slope of the line passing through the points (1, 2) and (1, 5).

Back

The slope is undefined because the x-coordinates are the same (1), indicating a vertical line.

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope is 4, which is the coefficient of x in the equation.

Front

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

Back

The slope is -2, which is the coefficient of x in the equation.