Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has 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 the y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

Front

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

Back

To find the x-intercept of a linear equation, set y = 0 and solve for x.

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 a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What is the significance of a zero slope?

Back

A zero slope indicates a horizontal line, meaning that the y-value remains constant regardless of the x-value.

Front

What is the significance of an undefined slope?

Back

An undefined slope indicates a vertical line, meaning that the x-value is constant and the line does not have a defined slope.

Front

How can you determine if a relation is 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, the relation is not a function.