Slope

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as 'm' in the equation y = mx + b.

Front

How is the slope calculated 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-value increases, the y-value also increases, resulting in an upward slant 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, resulting in a downward slant from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in the y-value 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

In the equation y = mx + b, what does 'b' represent?

Back

In the equation y = mx + b, 'b' represents the y-intercept, the point where the line crosses the y-axis.

Front

How can you determine the slope from a linear equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the slope is the coefficient of x, which is 'm'.

Front

What is the slope of the line represented by the equation y = -2x + 5?

Back

The slope of the line is -2.

Front

What is the slope of the line segment connecting points (1, 2) and (3, 6)?

Back

The slope is (6 - 2) / (3 - 1) = 4 / 2 = 2.