PSL January 7, 2025

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 'm' in the equation of a line (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

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 zero, indicating that there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero.

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 is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept represents the point where the line crosses the y-axis, which occurs when x = 0.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, the y-value increases by 3 units.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope, meaning they rise and fall at the same rate and never intersect.