Interpreting Slope and Y-Intercepts in Real-World Context

Front

What is the slope in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable, indicating how steep the line is.

Front

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

Back

The slope indicates how much the dependent variable changes for each unit increase in the independent variable, often representing a rate.

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the value of the dependent variable when the independent variable is zero, indicating the starting point of the relationship.

Front

How can you find the y-intercept from a linear equation in slope-intercept form (y = mx + b)?

Back

The y-intercept is the value of b in the equation, which is the point where the line crosses the y-axis.

Front

What does a positive slope indicate about a relationship between two variables?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate about a relationship between two variables?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

In the context of a taxi fare, what does the flat fee represent in the equation?

Back

The flat fee represents the initial cost of the ride before any distance is traveled.

Front

In the context of a swimming pool being filled, how can you determine the slope from a table of values?

Back

The slope can be determined by calculating the change in water volume over the change in time between two points.

Front

What does the y-intercept tell you in the context of a car descending a mountain?

Back

The y-intercept indicates the starting altitude of the car before it begins to descend.

Front

How do you interpret the y-intercept in a temperature vs. time graph during a chemical reaction?

Back

The y-intercept indicates the initial temperature of the solution at the start of the reaction.