Linear Functions Review

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 dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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

A line with an undefined slope is vertical. It does not rise or fall as it moves along the x-axis.

The slope (m) is calculated using the formula $$m = \frac{y2 - y1}{x2 - x1}$$ .

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

To determine the range from a graph, identify the lowest and highest points on the y-axis that the graph reaches.

A function is increasing if, as the x-values increase, the y-values also increase. This is indicated by a positive slope.

A function is decreasing if, as the x-values increase, the y-values decrease. This is indicated by a negative slope.

To convert to slope-intercept form, solve for y: $$3y = 2x + 9$$ , then $$y = \frac{2}{3}x + 3$$ .