Linear function graphs

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.

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is.

A positive slope means that as the x-value increases, the y-value also increases. The line rises from left to right.

A negative slope means that as the x-value increases, the y-value decreases. The line falls from left to right.

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

An undefined slope occurs in a vertical line where the x-value remains constant, and the y-value can change.

To find the y-intercept, set $$x = 0$$ in the equation and solve for $$y$$ .

The coordinates of the y-intercept are (0, y), where y can be any value. For $$x = -2$$ , the line does not cross the y-axis.

A line is increasing when the slope is positive, meaning that as you move from left to right, the y-values increase.

A line is decreasing when the slope is negative, meaning that as you move from left to right, the y-values decrease.