To find the slope-intercept form of the equation for the line, we can follow these steps, assuming we have the coordinates of two points where the line intersects the axes.
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Identify the Points: The points on the graph represent the number of seventh graders (y) and eighth graders (x) that attended the dance. Since you mentioned that a total of 275 students attended the dance, we can set up the equation based on this information. If one point is (0, 275), it means all 275 were seventh graders, and (275, 0) means all were eighth graders.
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Find the Slope (m): The slope of a line can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 275) and (275, 0): \[ m = \frac{0 - 275}{275 - 0} = \frac{-275}{275} = -1 \]
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Write the Equation in Slope-Intercept Form: The slope-intercept form is given by: \[ y = mx + b \] Here, \(m\) is the slope we calculated (\(-1\)), and \(b\) is the y-intercept (the point where the line crosses the y-axis, which happens at (0, 275)). Thus, \(b = 275\).
Putting it all together, we have: \[ y = -1x + 275 \]
Thus, the values that complete your slope-intercept form equation are:
- Slope \( m = -1 \)
- y-intercept \( b = 275 \)
So, the slope-intercept form of the equation for the line is: \[ y = -1x + 275 \]
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