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 the y-coordinate with respect to the x-coordinate. It indicates how steep the line is.

The slope (m) is calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ .

The slope of a horizontal line is 0.

The slope of a vertical line is undefined.

The Point-Slope form is given by $$y - y_1 = m(x - x_1)$$ , where $$m$$ is the slope and $$(x_1, y_1)$$ is a point on the line.

The Slope-Intercept form is $$y = -3x + 35$$ .

The y-intercept is 3, which is the value of $$y$$ when $$x = 0$$ .

Two lines are parallel if they have the same slope and will never intersect.

Two lines are perpendicular if the product of their slopes is -1.