Slopes

Front

What is the definition of slope?

Back

The slope is a measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

Slope (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, 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 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 is the x-intercept of a line?

Back

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

Front

What does it mean if the rate of change is constant?

Back

If the rate of change is constant, it means that the slope of the line is the same between any two points on the line.

Front

How can you determine the slope from a table of values?

Back

To determine the slope from a table, calculate the change in y divided by the change in x between two points.

Front

What is the formula for the equation of a line in slope-intercept form?

Back

The formula is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a line has a slope of 0, what does that indicate?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.