Functions: Warmups Part 1

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It shows how one variable changes in relation to another.

Front

What does the y-intercept represent in a linear graph?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of the dependent variable when the independent variable is zero.

Front

How do you determine the slope of a line in a graph?

Back

The slope of a line is determined by the change in the y-value divided by the change in the x-value (rise over run). It indicates how steep the line is.

Front

What does a steeper line indicate in a linear relationship?

Back

A steeper line indicates a greater rate of change between the two variables. For example, if one line is steeper than another, it means that variable changes more quickly.

Front

If Jerry saves $10 per week and starts with $0, what is the equation for his savings over time?

Back

The equation is Y = 10X, where Y is the total savings and X is the number of weeks.

Front

If Larry saves $10 per week and starts with $25, what is the equation for his savings over time?

Back

The equation is Y = 10X + 25, where Y is the total savings and X is the number of weeks.

Front

What is the significance of the initial amount in a savings problem?

Back

The initial amount affects the y-intercept of the graph, indicating how much money is available before any savings are added.

Front

How can you compare two linear relationships on a graph?

Back

You can compare their slopes and y-intercepts to understand which one increases faster and which one starts at a higher value.

Front

What does it mean if one line is above another on a graph?

Back

If one line is above another, it means that the variable represented by that line has a greater value at that point in time.

Front

In the context of spending from a gift card, what does a negative slope indicate?

Back

A negative slope indicates that the amount of money on the gift card is decreasing over time as money is spent.