Linear Functions Review

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.

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 and the direction it goes.

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

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

To convert from standard form $$Ax + By = C$$ to slope-intercept form $$y = mx + b$$ , solve for $$y$$ .

The slope-intercept form of a linear equation is $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

The equation of the line is $$y = -2x + 3$$ .

To find the y-intercept, set $$x = 0$$ and solve for $$y$$ . The y-intercept is $$\left(0, -\frac{1}{2}\right)$$ .

The graph of $$y = -x + 2$$ is a straight line with a slope of -1 and a y-intercept at (0, 2).

Using the equation $$y = 0.10x + 8$$ , set $$y = 52$$ and solve for $$x$$ . The solution is $$x = 440$$ .