Use the image to answer the question.

Question

A line with arrows at both ends connects two labeled points in a coordinate plane where the x- and y-axes range from 0 to 500 in increments of 125. The x-axis is labeled 'Eighth Graders' and the y-axis is labeled 'Seventh Graders.'

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

Answer 1

To determine the slope-intercept form of the equation of the line representing the number of seventh graders (y) and eighth graders (x) who attended the dance, we can use the information provided: a total of 275 students attended the dance.

In mathematical terms, this can be represented as: \[ x + y = 275 \]

Now, we need to express this equation in slope-intercept form, which is: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the original equation: \[ y = 275 - x \]

Now, we can rearrange it to fit the slope-intercept form: \[ y = -1x + 275 \]

Thus, the slope-intercept form of the equation is: \[ y = -x + 275 \]

From this, we can see that the slope \( m \) is -1 and the y-intercept \( b \) is 275.

To answer the question: The slope-intercept form of the equation for the line is: \[ y = -x + 275 \]