Standard Form (Ax + By = C)

Standard form of a linear equation is: [formula] where A, B, and C are constants (usually integers), and by convention A geq 0. Advantages of standard form: - Easy to find both intercepts - Natural form for many word problems - Used in systems of equations (elimination method) Finding intercepts: - X-intercept: set y = 0, solve for x → point (frac{C}{A}, 0) - Y-intercept: set x = 0, solve for y…

Example: Find the x- and y-intercepts of 3x + 4y = 12.

To convert from slope-intercept to standard form: 1. Move the x-term to the left side 2. If needed, multiply to clear fractions 3. Make sure A is positive

Example: Convert y = frac{2}{3}x - 4 to standard form.