Graph the inequality.
StartFraction x Over 5 EndFraction plus StartFraction y Over 4 EndFraction less than 1
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Part 1
Use the graphing tool to graph the inequality. 

The inequality you provided is:

\[
\frac{x}{5} + \frac{y}{4} < 1
\]

### Steps to graph the inequality:
1. **Rearrange into slope-intercept form**:
   To make it easier to graph, we'll first treat the inequality as an equation, \(\frac{x}{5} + \frac{y}{4} = 1\), and solve for \(y\).
   
   \[
   \frac{y}{4} = 1 - \frac{x}{5}
   \]

   Multiply both sides by 4 to solve for \(y\):

   \[
   y = 4 \left(1 - \frac{x}{5}\right) = 4 - \frac{4x}{5}
   \]

   Now we have \(y = 4 - \frac{4}{5}x\), which is the equation of the boundary line.

2. **Graph the boundary line**:
   This line is the boundary of the inequality. Since the inequality is "<" (less than), we'll use a **dashed line** to represent this. The slope is \(-\frac{4}{5}\), and the y-intercept is 4.

3. **Shading the region**:
   Since the inequality is \(\frac{x}{5} + \frac{y}{4} < 1\), we will shade **below** the line (the region where \(y\) is less than \(4 - \frac{4}{5}x\)).

4. **Identify intercepts**:
   To make it easier to graph the line, let's find the intercepts:
   - **x-intercept**: Set \(y = 0\) in the equation \(\frac{x}{5} + \frac{y}{4} = 1\):
     \[
     \frac{x}{5} = 1 \quad \Rightarrow \quad x = 5
     \]
   - **y-intercept**: Set \(x = 0\) in the equation \(\frac{x}{5} + \frac{y}{4} = 1\):
     \[
     \frac{y}{4} = 1 \quad \Rightarrow \quad y = 4
     \]

Thus, the boundary line will pass through the points \((5, 0)\) and \((0, 4)\).

### Graph:

I can graph this inequality for you as described, generating a graph where you will see a dashed line representing the boundary and shading below it.

Let me know if you'd like the graph! Would you also like a more detailed explanation on any of these steps?

Graph the inequality. StartFraction x Over 5 EndFraction plus StartFraction y Over 4 EndFraction less than 1

Learn how to graph the inequality x/5 + y/4 < 1 by rearranging it into slope-intercept form, graphing the boundary line, and shading the correct region. This solution covers key algebraic concepts suitable for students in Grades 8-10.

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