Slope from equations

Front

What is the slope of a line?

Back

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

Front

What does a positive slope indicate?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward trend on a graph.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward trend on a graph.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, meaning 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 0, leading to division by zero.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

What is the difference between positive and negative slopes?

Back

Positive slopes rise from left to right, while negative slopes fall from left to right.

Front

What does a slope of 1 mean?

Back

A slope of 1 means that for every unit increase in x, y increases by the same amount, resulting in a 45-degree angle.