Unit 3:Linear Functions Test Review

Front

What is the definition of a linear function?

Back

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

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

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 the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is the significance of a positive slope?

Back

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

Front

What is the significance of a negative slope?

Back

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

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the rate of change (slope) between any two points is constant. This can be checked by calculating the differences in y-values and x-values.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

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

Front

What does it mean if a line has a slope of zero?

Back

A slope of zero means that the line is horizontal, indicating that the dependent variable (y) does not change as the independent variable (x) changes.