Function Representations & Graphs Warmup

Front

What is a function in mathematics?

Back

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

Front

What does the slope (m) in the equation y = mx + b represent?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept (b) in the equation y = mx + b represent?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

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

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, characterized by a constant slope.

Front

How can you determine if a table of values represents a linear function?

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, it represents a linear function.

Front

What is the significance of the coordinates (0, b) in a linear graph?

Back

The coordinates (0, b) represent the y-intercept of the graph, where the line crosses the y-axis.

Front

What is the formula for finding the y-value given an x-value in a linear function?

Back

Substitute the x-value into the equation y = mx + b to find the corresponding y-value.