If \( (6,39) \) and \( (-5,-49) \) are two anchor points on a trend line, then find the equation of the line. \( y=[?] x+ \)
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To find the equation of the line passing through the points \( (6,39) \) and \( (-5,-49) \), we first calculate the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-49 - 39}{-5 - 6} = \frac{-88}{-11} = 8 \] Next, we can use the point-slope form of the equation of a line, \( y - y_1 = m(x - x_1) \), using one of the points, let's use \( (6, 39) \): \[ y - 39 = 8(x - 6) \] Distributing gives: \[ y - 39 = 8x - 48 \] Adding \( 39 \) to both sides: \[ y = 8x - 9 \] So, the equation of the line is \( y = 8x - 9 \).