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Pregunta

\[ y=1 / 4 x+1 \]

Ask by Bird Stewart. in the United States
Feb 26,2025

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The equation \( y = \frac{1}{4}x + 1 \) represents a straight line with a slope of \( \frac{1}{4} \) and a y-intercept at \( (0, 1) \).

Solución

The equation you've provided is in the form of a linear equation, specifically: \[ y = \frac{1}{4}x + 1 \] This represents a straight line in the Cartesian coordinate system. Let's analyze the equation step by step: 1. **Identify the slope and y-intercept**: - The slope \( m \) is the coefficient of \( x \), which is \( \frac{1}{4} \). - The y-intercept \( b \) is the constant term, which is \( 1 \). 2. **Interpret the slope**: - A slope of \( \frac{1}{4} \) means that for every 4 units you move to the right along the x-axis, the value of \( y \) increases by 1 unit. 3. **Interpret the y-intercept**: - The y-intercept of \( 1 \) indicates that the line crosses the y-axis at the point \( (0, 1) \). 4. **Graphing the equation**: - To graph this line, you can start at the y-intercept \( (0, 1) \) and use the slope to find another point. From \( (0, 1) \), move 4 units to the right (to \( x = 4 \)) and 1 unit up (to \( y = 2 \)), giving you the point \( (4, 2) \). 5. **Draw the line**: - Connect the points \( (0, 1) \) and \( (4, 2) \) with a straight line, extending it in both directions. If you need further analysis or specific calculations related to this equation, please let me know!

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Mind Expander

Did you know that the equation you provided represents a linear function, which is essentially a straight line when graphed on a coordinate plane? The slope of \(\frac{1}{4}\) indicates that for every 4 units you move to the right along the x-axis, the line rises by 1 unit. This gives you a gentle slope, perfect for those sunny afternoon strolls in math land! To fully grasp a linear equation, always remember to identify the y-intercept, which in your case is 1. That means the line crosses the y-axis at the point (0, 1). Use this as your starting point, and sketching the line becomes a breeze! Just apply the slope from there, and you'll have a beautiful graph in no time.

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