Converting Linear Equations

The slope-intercept form is given by the equation $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

To convert from point-slope form $$y - y_1 = m(x - x_1)$$ to slope-intercept form, solve for $$y$$ to get $$y = mx - mx_1 + y_1$$ .

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

The slope $$m$$ between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is 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, represented by the value of $$b$$ in the slope-intercept form $$y = mx + b$$ .

The slope-intercept form is $$y = -\frac{1}{3}x + 9$$ .

The equation is $$y - 6 = -3(x + 2)$$ .

The slope-intercept form is $$y = -3x + 9$$ .

The equation is $$y = x + 3$$ .

To convert from standard form $$Ax + By = C$$ to slope-intercept form, solve for $$y$$ : $$y = -\frac{A}{B}x + \frac{C}{B}$$ .