Linear Functions Review

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, defined 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

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the formula slope (m) = rise/run.

Front

What is 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 is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What is the significance of a zero slope?

Back

A zero slope indicates a horizontal line, meaning there is no change in y as x changes; the function has a constant value.

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, it is not a function.

Front

What is a function in mathematical terms?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

How can you convert a standard form equation to slope-intercept form?

Back

To convert a standard form equation (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What does it mean for a set of values to represent a function?

Back

A set of values represents a function if each input (x-value) is associated with exactly one output (y-value).