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# How to Figure Out at What Time I Should Write Which Linear Equation Form Choosing the right equation form depends on the given information and the problem context. ## 1. Slope-Intercept Form: $y = mx + b$ * **Use when:** You know the slope (m) and y-intercept (b). * **The problem involves:** In...

# How to Figure Out at What Time I Should Write Which Linear Equation Form Choosing the right equation form depends on the given information and the problem context. ## 1. Slope-Intercept Form: $y = mx + b$ * **Use when:** You know the slope (m) and y-intercept (b). * **The problem involves:** Interpreting the rate of change and initial value. * **Example:** A phone plan costs $10 per month with a $50 startup fee. $y = 10x + 50$ ## 2. Point-Slope Form: $y - y_{1} = m(x - x_{1})$ * **Use when:** You know one point $(x_{1}, y_{1})$ and the slope (m). * **Use when:** You need to quickly write an equation without finding the y-intercept. * **Example:** A line passes through (3, 5) with a slope of 2. $y - 5 = 2(x - 3)$ ## 3. Standard Form: $Ax + By = C$ * **Use when:** You want integer coefficients for a cleaner equation. * **Use when:** The problem involves constraints, such as real-world contexts where negative values don't make sense (e.g., money, inventory). * **Example:** A truck can carry 4 boxes and 5 barrels, with a max load of 100. $4x + 5y = 100$ ### Summary Table | Form | Best When | Example | |-----------------|-----------------------------------------------------------------------------------|-------------------------------------------------| | Slope-Intercept | You have the slope and y-intercept | Cost per month problem | | Point-Slope | You have a point and slope | Car fuel level over distance | | Standard | Word problems, integer coefficients | Sales constraints |