Equation: $$ y=\frac{3}{8} x+3 $$

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1. **Identify the form of the equation**

The equation 
   
   $$
   y=\frac{3}{8}x+3
   $$
   
   is in slope-intercept form, which is 
   
   $$
   y = mx + b,
   $$
   
   where $$ m $$ is the slope and $$ b $$ is the $$ y $$-intercept.

2. **Determine the slope and $$ y $$-intercept**

- The slope is 
     
     $$
     m=\frac{3}{8}.
     $$
     
   - The $$ y $$-intercept is 
     
     $$
     b=3.
     $$
     
     This means the line crosses the $$ y $$-axis at the point $$(0, 3)$$.

3. **Find the $$ x $$-intercept**

To find the $$ x $$-intercept, set $$ y=0 $$ and solve for $$ x $$:
   
   $$
   0=\frac{3}{8}x+3.
   $$
   
   Multiply each term by 8 to eliminate the fraction:
   
   $$
   0=3x+24.
   $$
   
   Solve for $$ x $$:
   
   $$
   3x=-24 \quad\Rightarrow\quad x=-8.
   $$
   
   So, the $$ x $$-intercept is $$(-8, 0)$$.

4. **Summary**

- **Slope:** $$\frac{3}{8}$$
   - **$$ y $$-intercept:** $$(0, 3)$$
   - **$$ x $$-intercept:** $$(-8, 0)$$

This breakdown explains all the important features of the linear equation.
The equation $$ y = \frac{3}{8}x + 3 $$ has a slope of $$ \frac{3}{8} $$, a $$ y $$-intercept at $$(0, 3)$$, and an $$ x $$-intercept at $$(-8, 0)$$.

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