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 is the slope of a line?

Back

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

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

How can you determine if a table of values represents a function?

Back

A table represents a function if no x-value is repeated; each x-value must correspond to only one y-value.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for that function.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What does it mean for a graph to be nonlinear?

Back

A graph is nonlinear if it does not form a straight line, indicating that the relationship between the variables is not constant.

Front

How do you identify a function from a graph?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the equation of a line with a slope of -1 and a y-intercept of 2?

Back

The equation is y = -x + 2.