Interpreting Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is a y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the coordinates (0, b) in the equation y = mx + b.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Front

What is a scatter plot?

Back

A scatter plot is a graph that shows the relationship between two variables by displaying data points on a Cartesian plane.

Front

What does a trend line represent in a scatter plot?

Back

A trend line is a straight line that best represents the data points in a scatter plot, indicating the general direction of the data.

Front

How can you use a trend line to make predictions?

Back

You can use a trend line to estimate the value of one variable based on the value of another by finding the corresponding point on the line.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.