Slope and Intercepts

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 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-value increases, the y-value also increases, resulting in an upward slant.

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.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-values are the same for two points, leading to division by zero.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

How can you identify a line with the steepest slope?

Back

The steepness of a slope is determined by the absolute value of the slope; the larger the absolute value, the steeper the line.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in the y-value as the x-value changes.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope; they never intersect and maintain a constant distance apart.

Front

What is the relationship between slope and perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other; if one slope is m, the other is -1/m.