Question
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For the following line the \( x \)-intercept and the \( y \)-intercept are both 0 , which means the graph will go through the origin, \( (0,0) \). Graph the line by finding a point other than the origin, and then drawing a line through that point and the origin. \( y=\frac{1}{3} x \)

Ask by Romero Boyd. in the United States
Mar 20,2025

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Tutor-Verified Answer

Answer

To graph the line \( y = \frac{1}{3}x \), plot the origin \( (0,0) \) and another point like \( (3,1) \), then draw a straight line through these two points.

Solution

1. **Determine the intercepts:** The \(x\)-intercept is found by setting \( y = 0 \) in the equation: \[ 0 = \frac{1}{3}x \implies x = 0. \] Thus, the \(x\)-intercept is \( (0,0) \). The \(y\)-intercept is found by setting \( x = 0 \): \[ y = \frac{1}{3}(0) = 0. \] Thus, the \(y\)-intercept is \( (0,0) \). 2. **Find another point on the line:** Choose a value for \( x \) that is not 0. For example, let \( x = 3 \). Substitute into the equation: \[ y = \frac{1}{3}(3) = 1. \] This gives the point \( (3,1) \). 3. **Graphing the line:** - Plot the origin \( (0,0) \). - Plot the point \( (3,1) \). - Draw a straight line through \( (0,0) \) and \( (3,1) \). The resulting graph represents the line \( y = \frac{1}{3}x \).

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Extra Insights

To graph the line \( y = \frac{1}{3} x \), you can choose an easy point to find another point on the line. If you set \( x = 3 \), you get \( y = \frac{1}{3} \cdot 3 = 1 \). So, another point on the line is \( (3,1) \). Plot both the origin \( (0,0) \) and the point \( (3,1) \), then draw a straight line through these two points to complete the graph. Remember, the slope of \( \frac{1}{3} \) indicates that for every 3 units you move to the right (increase in \( x \)), you only move 1 unit up (increase in \( y \)). This subtle relationship tells you how gently the line will rise as it extends through the coordinate plane!

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