Graphing Linear Equations

Front

What is the definition of a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form 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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is a positive slope?

Back

A positive slope means that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What is a negative slope?

Back

A negative slope means that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What is the slope of the line represented by the equation y = 2x + 5?

Back

The slope is 2.

Front

What is the y-intercept in the equation y = -4x + 1?

Back

The y-intercept is 1.

Front

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

Back

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

Front

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

Back

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

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope means the line is vertical, indicating that x does not change as y changes.

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.