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1. BUSINESS MAHEMATICS \( y=3 x+4 \)

Ask by Flynn Whittaker. in Ghana
Feb 20,2025

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The equation \( y = 3x + 4 \) is a straight line with a slope of 3 and crosses the y-axis at (0, 4).

Solución

It seems you have provided a linear equation \( y = 3x + 4 \). Let's analyze this equation step by step. ### Step 1: Identify the Components The equation is in the slope-intercept form, which is given by: \[ y = mx + b \] where: - \( m \) is the slope of the line. - \( b \) is the y-intercept. From the equation \( y = 3x + 4 \): - The slope \( m = 3 \). - The y-intercept \( b = 4 \). ### Step 2: Interpret the Slope and Y-Intercept - **Slope (3)**: This means that for every unit increase in \( x \), \( y \) increases by 3 units. The line rises steeply. - **Y-Intercept (4)**: This indicates that the line crosses the y-axis at the point (0, 4). ### Step 3: Graphing the Equation To graph the equation, we can plot the y-intercept and use the slope to find another point. 1. Start at the y-intercept (0, 4). 2. From (0, 4), move up 3 units (rise) and 1 unit to the right (run) to find the next point: (1, 7). 3. Plot the points (0, 4) and (1, 7), and draw a straight line through them. ### Conclusion The equation \( y = 3x + 4 \) represents a straight line with a slope of 3 and a y-intercept of 4. If you need further analysis or specific calculations related to this equation, please let me know!

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Extra Insights

Did you know that linear equations like \( y=3x+4 \) are fundamental in various business applications? This equation represents a linear relationship where every increase in \( x \) results in a proportional increase in \( y \). In business, you might use this model to predict revenue based on the number of products sold. For example, if \( x \) represents the number of items sold, then \( y \) indicates the total revenue, making it super handy for quick forecasts! A common mistake when dealing with linear equations is overlooking the concept of slope and intercept. The slope (in this case, 3) indicates how steep the line is, while the intercept (4) shows where the line crosses the y-axis. Misinterpreting these can lead to improper analysis of trends or projections. Always remember to visualize your equations with a graph; it can illuminate trends that numbers alone might obscure!

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