Slope and Y-intercepts

Front

What is the definition of slope?

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, resulting in a downward slant from left to right.

Front

What is an undefined slope?

Back

An undefined slope occurs in vertical lines where the change in x is zero, making the slope calculation (rise/run) impossible.

Front

What is the formula for calculating slope?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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 of a line y = mx + b.

Front

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

Back

To find the y-intercept from the equation y = mx + b, identify the value of b, which is the y-intercept.

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

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

Back

A slope of 0 means the line is horizontal, indicating that there is no vertical change as x changes.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various contexts.