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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?

1 answer

To derive the equation in slope-intercept form (y = mx + b) for the values representing seventh graders and eighth graders attending the dance, we need more information about the graph, such as the number of students from each grade or specific data points.

Assuming the graph shows a linear relationship between the number of seventh graders (let's denote this as \(x\)) and the number of eighth graders (denote this as \(y\)), we can start by noting the total attendance:

  1. Total students: \( x + y = 275 \)

To convert this equation into slope-intercept form:

  • Rearranging gives \( y = 275 - x \)

Now, interpreting this in terms of slope-intercept form:

  • \( y = -1x + 275 \)

Here:

  • The slope \( m \) is -1, indicating that for every additional seventh grader, there is one fewer eighth grader, given the total attendance constraint.
  • The y-intercept \( b \) is 275, which represents the maximum number of eighth graders that could attend if no seventh graders attended.

If you have specific numbers or coordinates from the graph, please provide those for a more accurate calculation or explanation.