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

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:  *(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.