Graphing linear Functions

Front

What is a linear function?

Back

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

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) 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 (b) in a linear equation?

Back

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

Front

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

Back

The slope (m) can be 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, and A should be non-negative.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1 (m1 * m2 = -1).

Front

What is the graphical representation of the equation y = mx + b?

Back

The equation y = mx + b represents a straight line on a graph, where m is the slope and b is the y-intercept.

Front

What does it mean for a linear function to be increasing?

Back

A linear function is increasing if its slope (m) is positive, meaning as x increases, y also increases.

Front

What does it mean for a linear function to be decreasing?

Back

A linear function is decreasing if its slope (m) is negative, meaning as x increases, y decreases.