5.6 Transforming Linear Equations

Front

What is the parent graph of linear equations?

Back

The parent graph of linear equations is the graph of the equation y = x.

Front

How does the slope of a linear equation affect its steepness?

Back

A larger absolute value of the slope indicates a steeper graph, while a smaller absolute value indicates a less steep graph.

Front

What transformation occurs when a linear equation has a positive y-intercept?

Back

The graph shifts upward by the value of the y-intercept.

Front

What transformation occurs when a linear equation has a negative y-intercept?

Back

The graph shifts downward by the value of the y-intercept.

Front

How does the coefficient of x in a linear equation affect the graph?

Back

The coefficient of x (slope) determines the steepness and direction of the graph; positive slopes rise to the right, while negative slopes fall to the right.

Front

What does it mean for a graph to be 'steeper'?

Back

A graph is 'steeper' when it has a larger absolute value of slope, indicating a sharper incline or decline.

Front

What does it mean for a graph to be 'less steep'?

Back

A graph is 'less steep' when it has a smaller absolute value of slope, indicating a gentler incline or decline.

Front

What is the effect of a vertical shift on the graph of a linear equation?

Back

A vertical shift moves the graph up or down without changing its slope.

Front

How do you identify a vertical shift in a linear equation?

Back

A vertical shift can be identified by the constant term added or subtracted from the equation (e.g., y = mx + b).

Front

What transformation occurs when the slope of a linear equation is negative?

Back

The graph slopes downward from left to right.