EOC Review: Applications of Linear Functions

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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 f(x) = 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 unit change 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.

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How do you interpret a strong positive correlation coefficient (r)?

Back

A strong positive correlation coefficient (r close to 1) indicates that as one variable increases, the other variable also tends to increase.

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How do you interpret a strong negative correlation coefficient (r)?

Back

A strong negative correlation coefficient (r close to -1) indicates that as one variable increases, the other variable tends to decrease.

Front

What does a correlation coefficient of 0 indicate?

Back

A correlation coefficient of 0 indicates no linear relationship between the two variables.

Front

What is the formula for calculating the total cost (y) for purchasing x tickets if there is a flat fee?

Back

The total cost can be represented as y = mx + b, where m is the cost per ticket and b is the flat fee.

Front

How can you determine the equation of a line given two points?

Back

To determine the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1), then use the point-slope form to find the equation.

Front

What is the significance of the correlation coefficient in data analysis?

Back

The correlation coefficient quantifies the strength and direction of a linear relationship between two variables, helping to understand how they are related.

Front

What does it mean if a function models data well?

Back

If a function models data well, it means that the function accurately represents the relationship between the variables and can be used to make predictions.