Linear Relationships

Front

What is the definition of slope in a linear relationship?

Back

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

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 linear relationship?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

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

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean if two lines intersect at a point?

Back

If two lines intersect at a point, it means they have different slopes and will meet at that specific point.

Front

In the context of a real-world problem, what does the y-intercept represent?

Back

The y-intercept represents the initial value or starting point of the dependent variable when the independent variable is zero.

Front

How do you interpret the slope in a real-world context?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.