Writing Linear Equations

A linear equation is an equation that makes a straight line when graphed. It can be written in 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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

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

The equation of a horizontal line is of the form $$y = c$$ , where $$c$$ is a constant value.

The equation of a vertical line is of the form $$x = c$$ , where $$c$$ is a constant value.

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

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

The slope of a horizontal line is 0.

The slope of a vertical line is undefined.