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. \( y=\frac{1}{3} x \)
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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!