Graph the equation. $$ y=3 x-1 $$

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1. Write the equation in slope-intercept form:
   $$
   y=3x-1,
   $$
   where the slope is $$ m=3 $$ and the $$ y $$-intercept is $$ b=-1 $$.

2. Identify the $$ y $$-intercept:
   - When $$ x=0 $$, then $$ y=-1 $$.  
   - Plot the point $$(0,-1)$$.

3. Use the slope to find another point:
   - The slope $$ m=3 $$ means that for every increase of $$ 1 $$ unit in $$ x $$, $$ y $$ increases by $$ 3 $$ units.
   - Starting from $$(0,-1)$$, increase $$ x $$ by $$ 1 $$ to get $$ x=1 $$ and increase $$ y $$ by $$ 3 $$ to get $$ y=2 $$.
   - Plot the point $$(1,2)$$.

4. Draw the line:
   - Draw a straight line through the points $$(0,-1)$$ and $$(1,2)$$.  
   - Extend the line in both directions to complete the graph.

5. Optionally, find the $$ x $$-intercept:
   - Set $$ y=0 $$ in the equation:
     $$
     0=3x-1.
     $$
   - Solve for $$ x $$:
     $$
     3x=1 \quad \Rightarrow \quad x=\frac{1}{3}.
     $$
   - Plot the point $$\left(\frac{1}{3},0\right)$$ to verify the graph.

The line representing $$ y=3x-1 $$ should pass through all these points.
To graph the equation $$ y=3x-1 $$: 1. **Plot the y-intercept** at $$(0, -1)$$. 2. **Use the slope** $$ m=3 $$ to find another point: from $$(0, -1)$$, move up 3 units and right 1 unit to $$(1, 2)$$. 3. **Draw a straight line** through these points. 4. **Optional**: Find the x-intercept at $$\left(\frac{1}{3}, 0\right)$$ by setting $$ y=0 $$ and solving for $$ x $$. This will give you the graph of the equation $$ y=3x-1 $$.

Graph the equation. \( y=3 x-1 \)

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