8.AF.6 (part 1)

Front

What is the rate of change in a linear equation?

Back

The rate of change in a linear equation represents how much the dependent variable (y) changes for a unit change in the independent variable (x). It is often represented by the slope (m) in the equation y = mx + b.

Front

How do you find the rate of change from two points?

Back

To find the rate of change (slope) between two points (x1, y1) and (x2, y2), use the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the y-intercept of a linear equation?

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 can you identify the y-intercept from an equation?

Back

In the equation y = mx + b, the y-intercept is the value of b.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does the slope of a line represent?

Back

The slope of a line represents the steepness and direction of the line, indicating how much y changes for a unit change in x.

Front

How do you write an equation from a word problem?

Back

To write an equation from a word problem, identify the variables, determine the relationship between them, and express it mathematically.

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

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

Back

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