1. Let's start by recalling the point-slope form of a line: $$y - y_1 = m(x - x_1)$$ where $(x_1,y_1)$ is a point on the line and $m$ is the slope. 2. The standard form of a line is generally written as: $$Ax + By = C$$ where $A$, $B$, and $C$ are integers and $A \geq 0$. 3. To switch from point-slope to standard form, first expand the right-hand side of the point-slope equation: $$y - y_1 = m(x - x_1) \implies y - y_1 = mx - mx_1$$ 4. Next, add $y_1$ to both sides to isolate $y$: $$y = mx - mx_1 + y_1$$ 5. To get to standard form, rearrange to get all terms involving variables $x$ and $y$ on one side and constants on the other: $$y - mx = y_1 - mx_1$$ 6. Multiply both sides by a common denominator if necessary to eliminate any fractions in $m$. 7. Finally, write the equation as $$Ax + By = C$$ making sure $A$ is positive and all coefficients are integers. For example, if we have the point-slope form: $$y - 2 = 3(x - 1)$$ Expand: $$y - 2 = 3x - 3$$ Add $2$ to both sides: $$y = 3x - 1$$ Rearrange: $$-3x + y = -1$$ Multiply both sides by $-1$ to make $A$ positive: $$3x - y = 1$$ which is the standard form. This process allows you to switch smoothly from point-slope to standard form.