Key Features of Linear Equations

Front

What happens to y when x is decreasing in a linear equation with a constant y-value?

Back

y stays constant.

Front

What is the domain of a linear function?

Back

All real numbers, represented as (-∞, ∞) or {x | x ∈ R}.

Front

In which interval is the graph of a linear function positive if it crosses the x-axis at x=1?

Back

x > 1.

Front

What does it mean for a graph to be increasing?

Back

As x increases, y also increases.

Front

What is the y-intercept of the equation y = 3x - 12?

Back

(0, -12).

Front

What is the slope of a linear equation?

Back

The slope indicates the steepness of the line, calculated as the change in y over the change in x.

Front

How do you find the x-intercept of a linear equation?

Back

Set y to 0 and solve for x.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.

Front

What does a negative slope indicate about a linear function?

Back

As x increases, y decreases.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis.