Modeling Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function 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 one-unit increase in x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What does a positive correlation indicate in a graph?

Back

A positive correlation indicates that as one variable increases, the other variable also increases. The graph will slope upwards from left to right.

Front

What does a negative correlation indicate in a graph?

Back

A negative correlation indicates that as one variable increases, the other variable decreases. The graph will slope downwards from left to right.

Front

What is the meaning of the slope in the equation y = -2x + 7?

Back

In the equation y = -2x + 7, the slope of -2 means that for each hour of mowing, the mower is predicted to use 2 gallons of gas.

Front

How do you determine the correlation from a scatter plot?

Back

To determine the correlation from a scatter plot, observe the direction of the points: if they trend upwards, it's positive; if they trend downwards, it's negative; if they are scattered without a clear trend, there is no correlation.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) between two points is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a graph has no correlation?

Back

If a graph has no correlation, it means there is no predictable relationship between the two variables. The points are scattered randomly.

Front

What is the significance of the x-intercept in a linear function?

Back

The x-intercept is the value of x when y is 0. It is the point where the line crosses the x-axis.