Graph the line. $$ y=-\frac{1}{3} x+2 $$

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UpStudy AI · Accepted Answer

1. **Identify the y-intercept:**  
   The y-intercept is given by $$ (0, b) $$ where $$ b = 2 $$. So the y-intercept is  
   $$
   (0, 2)
   $$

2. **Determine the slope:**  
   The slope $$ m $$ of the line is $$-\frac{1}{3}$$. This means that for every increase of $$3$$ units in $$ x $$, the value of $$ y $$ decreases by $$1$$ unit.

3. **Plot additional points using the slope:**  
   - Starting from $$ (0, 2) $$, move $$3$$ units to the right (increase $$ x $$ by $$3$$) and $$1$$ unit down (decrease $$ y $$ by $$1$$). This gives the point  
     $$
     (3, 1)
     $$
   - Alternatively, move $$3$$ units to the left (decrease $$ x $$ by $$3 $$) and $$1$$ unit up (increase $$ y $$ by $$1$$). This gives the point  
     $$
     (-3, 3)
     $$

4. **Draw the line:**  
   Plot the points $$ (0, 2) $$, $$ (3, 1) $$, and $$ (-3, 3) $$ on the coordinate plane. Connect these points with a straight line, and extend the line in both directions.

5. **Label the line:**  
   Optionally, label the line as  
   $$
   y = -\frac{1}{3}x + 2
   $$  
   for clarity.
To graph the line $$ y = -\frac{1}{3}x + 2 $$, follow these steps: 1. **Find the y-intercept:** When $$ x = 0 $$, $$ y = 2 $$. So, plot the point $$ (0, 2) $$. 2. **Use the slope to find another point:** The slope is $$-\frac{1}{3}$$. Move 3 units to the right and 1 unit down from $$ (0, 2) $$ to get $$ (3, 1) $$. 3. **Plot the points and draw the line:** Plot $$ (0, 2) $$ and $$ (3, 1) $$, then draw a straight line through them. 4. **Optional:** Label the line as $$ y = -\frac{1}{3}x + 2 $$ for clarity.

Graph the line.

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