Slope and y-intercept

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the change in y (vertical) divided by the change in x (horizontal).

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula is: Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y 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 x increases, y decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs with vertical lines, where x does not change but y does, leading to division by zero in the slope formula.

Front

How do you find the y-intercept from the slope-intercept form of a line?

Back

In the slope-intercept form y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

What is the slope of the line that passes through the points (4, 5) and (4, 9)?

Back

The slope is undefined, as both points have the same x-coordinate.

Front

If a line has a slope of -3, what does this tell you about the line's direction?

Back

The line falls steeply from left to right, indicating a negative relationship between x and y.