Linear vs Non Linear Equations

Front

What is a linear equation?

Back

An equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear equation?

Back

An equation that does not form a straight line when graphed, such as quadratic equations (y = ax^2 + bx + c) or exponential equations.

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The set of all possible output values (y-values) for the function.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if different inputs produce different outputs.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What is a graph of a linear equation?

Back

A straight line that represents all the solutions of the equation.

Front

What is a graph of a non-linear equation?

Back

A curve that represents all the solutions of the equation, which can take various shapes like parabolas or circles.