Graph the inequality. $$ 5 x+2 y \leq 8 $$ Select an option for your boundary line: solid line Turn on the shading option and move the black point to show where to shade the half plane. dashed line

Question

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To graph the inequality $$ 5x + 2y \leq 8 $$, follow these steps:

1. **Graph the Boundary Line:**
   - **Equation of the Boundary Line:** Start by treating the inequality as an equation:
     $$
     5x + 2y = 8
     $$
   - **Find Intercepts:**
     - **x-intercept:** Let $$ y = 0 $$:
       $$
       5x = 8 \implies x = \frac{8}{5} = 1.6
       $$
       So, the x-intercept is at $$ (1.6, 0) $$.
     - **y-intercept:** Let $$ x = 0 $$:
       $$
       2y = 8 \implies y = 4
       $$
       So, the y-intercept is at $$ (0, 4) $$.

- **Draw the Line:**
     - Plot the points $$ (1.6, 0) $$ and $$ (0, 4) $$ on the coordinate plane.
     - **Choose a Solid or Dashed Line:**
       - Since the inequality is $$ \leq $$ (less than or equal to), **use a **solid line** to indicate that points on the line are included in the solution set.

2. **Shade the Appropriate Region:**
   - **Determine the Shading Direction:**
     - The inequality $$ 5x + 2y \leq 8 $$ can be rewritten in terms of $$ y $$:
       $$
       2y \leq -5x + 8 \implies y \leq -\frac{5}{2}x + 4
       $$
     - This means you will shade **below** the boundary line.
   
   - **Shading Steps:**
     - **Turn on the shading option** in your graphing tool or, if drawing by hand, use a pencil to lightly shade the area.
     - **Move the shading indicator** (the "black point") to ensure that the shaded region is below the solid boundary line.

3. **Final Graph:**
   - Your final graph should display a solid line passing through $$ (1.6, 0) $$ and $$ (0, 4) $$, with the area below this line shaded to represent all the points $$ (x, y) $$ that satisfy $$ 5x + 2y \leq 8 $$.

**Summary of Choices:**
- **Boundary Line:** **Solid Line**
- **Shading:** **Below the boundary line**

Here's a visual representation for clarity:

![Graph of 5x + 2y ≤ 8](https://i.imgur.com/yourImageLink.png) *(Please replace with an actual graph if available.)*

If you have access to a graphing tool, follow these steps to select a **solid line** and **shade below** the line accordingly.
To graph the inequality $$ 5x + 2y \leq 8 $$, draw a **solid line** for the boundary and shade the area **below** the line.

Graph the inequality.

Select an option for your boundary line:
solid line
Turn on the shading option and move the black point to show
where to shade the half plane.
dashed line

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Graph the inequality. Select an option for your boundary line: solid line Turn on the shading option and move the black point to show where to shade the half plane. dashed line