Interpreting Slope and Y-intercept

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is equal to zero. It represents the starting point of the line on the y-axis.

Front

In the equation y = mx + b, what do m and b represent?

Back

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

Front

How can you interpret a negative slope in a real-world context?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases. For example, if a tank is losing water, the negative slope shows the rate at which the water level drops.

Front

What does a slope of 0 indicate in a linear relationship?

Back

A slope of 0 indicates that there is no change in the dependent variable as the independent variable changes, resulting in a horizontal line.

Front

How do you calculate 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 is the significance of the y-intercept in a real-world scenario?

Back

The y-intercept provides a starting value for the dependent variable when the independent variable is zero, helping to understand initial conditions.

Front

How does the slope relate to speed in a distance-time graph?

Back

In a distance-time graph, the slope represents speed; a steeper slope indicates a higher speed.

Front

What does it mean if the y-intercept is a negative value?

Back

A negative y-intercept indicates that the initial value of the dependent variable is below zero when the independent variable is zero, which may not be physically meaningful in some contexts.

Front

How can you interpret the slope in the context of a cost function?

Back

In a cost function, the slope indicates the additional cost incurred for each additional unit produced or consumed.