Linear Key Features

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise/run).

Front

How do you calculate the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y 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 x increases, y 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

How can you find the y-intercept from the slope-intercept form of a linear equation?

Back

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

Front

What does the slope represent in a real-world context?

Back

In a real-world context, the slope represents the rate of change between two variables, such as speed or efficiency.

Front

How do you interpret the slope in the context of a problem involving distance and time?

Back

The slope represents the speed or rate of movement, indicating how much distance is covered per unit of time.

Front

What is the significance of the x- and y-intercepts in a graph?

Back

The x- and y-intercepts provide key points that help in graphing the line and understanding its behavior.