Compare Linear Functions: Graph to Equation

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 linear function represent?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

How do you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line, calculating the rise (change in y) over the run (change in x).

Front

What is the y-intercept in 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

If a linear function has a positive slope, what does that indicate about the graph?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the graph.

Front

If a linear function has a negative slope, what does that indicate about the graph?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the graph.

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they are parallel and will never intersect.

Front

How can you tell which function has a greater slope from their equations?

Back

You can compare the coefficients of x in the equations; the function with the larger coefficient has the greater slope.

Front

What is the significance of the slope being zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

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

Back

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