If \( (-7,43) \) and \( (4,-12) \) are two anchor points on a trend line, then find the equation of the line. \( \qquad y=[?] x+\square] \)
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To find the equation of the line that passes through the points \( (-7, 43) \) and \( (4, -12) \), we first calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-12 - 43}{4 - (-7)} = \frac{-55}{11} = -5. \] Now that we have the slope, we can use point-slope form to find the equation of the line. Let's use the point \( (-7, 43) \): \[ y - 43 = -5(x + 7). \] Distributing gives us: \[ y - 43 = -5x - 35. \] Adding 43 to both sides: \[ y = -5x + 8. \] The equation of the line is \[ y = -5x + 8. \] So, in the requested format: \( y = [-5] x + [8] \).
