Slope

Front

What is the definition of slope in a linear equation?

Back

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

Front

How do you identify the slope and y-intercept from the equation of a line in slope-intercept form (y = mx + b)?

Back

In the equation y = mx + b, 'm' represents the slope and 'b' represents the y-intercept.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

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

Back

The slope (m) can be calculated using the formula 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

How do you convert the equation from standard form (Ax + By = C) to slope-intercept form (y = mx + b)?

Back

To convert to slope-intercept form, solve for y: isolate y on one side of the equation.

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.