Find the equation of a line in slope-intercept form

The slope-intercept form of a linear equation is given by the formula: $$y = mx + b$$ , 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 slope means the line rises, negative slope means it falls).

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

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

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

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

An undefined slope indicates that the line is vertical, meaning there is no change in x as y changes.

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Two lines are perpendicular if the product of their slopes is -1. If one line has a slope of $$m$$ , the other line's slope must be $$-\frac{1}{m}$$ .

Using the point-slope form, the equation is $$y - 2 = 3(x - 1)$$ , which simplifies to $$y = 3x - 1$$ .