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?

Question

(1 point)
The slope-intercept form of the equation for the line is y=
x+
.

Answer 1

To express the relationship between the number of seventh graders \( x \) and the number of eighth graders \( y \) who attended the dance, we start with the information that the total attendance was 275 students.

Therefore, we can set up the equation:

\[ x + y = 275 \]

To convert this equation into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we need to solve for \( y \):

1. Start with the equation: \[ x + y = 275 \]

2. Subtract \( x \) from both sides: \[ y = -x + 275 \]

In this form, the slope \( m \) is \(-1\) and the y-intercept \( b \) is \( 275 \).

Thus, the equation in slope-intercept form is:

\[ y = -1x + 275 \]

So in the context of your question, the answer would be:

The slope-intercept form of the equation for the line is \( y = -x + 275 \).