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Last Friday, East Middle School held a homecoming dance for the seventh-grade and eighth-grade students. In all, 275 students attended the dance. The graph represents how many possible seventh graders and how many possible eighth graders attended the dance. What values will complete the equation for the graph in slope-intercept form?

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To find the values that will complete the equation in slope-intercept form, we first need to understand the situation described.

Let’s define the variables:

  • Let \( y \) represent the number of seventh graders who attended the dance.
  • Let \( x \) represent the number of eighth graders who attended the dance.

From the problem, we know that the total number of students (both seventh graders and eighth graders) who attended the dance is 275. This gives us the equation:

\[ y + x = 275 \]

To put this equation into slope-intercept form, we need to express it as \( y = mx + b \). We can rearrange the equation as follows:

  1. Subtract \( x \) from both sides:

\[ y = 275 - x \]

Now, this equation \( y = -x + 275 \) is in slope-intercept form, where:

  • The slope (\( m \)) is -1,
  • The y-intercept (\( b \)) is 275.

In the context of your question about completing the graph with certain values, the values you would be looking for that represent the slope and intercept in the equation \( y = -x + 275 \) are:

  1. The slope (m): -1
  2. The y-intercept (b): 275

If you need specific values or points to plot for the graph, you can choose various values for \( x \) (the number of eighth graders) and calculate the corresponding \( y \) (the number of seventh graders) using this equation. For instance:

  • If \( x = 0 \): \( y = 275 \) (All seventh graders)
  • If \( x = 100 \): \( y = 175 \)
  • If \( x = 275 \): \( y = 0 \) (All eighth graders)

These points can help to plot the line represented by the equation on a graph.