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To find the equation of the line passing through the points (6, –3) and (–4, –9), we can first find the slope of the line using the formula:
slope = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Using the coordinates of the points, we have:
slope = (-9 - (-3)) / (-4 - 6) = (-9 + 3) / (-10) = -6 / -10 = 3/5
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Let's use the point (6, -3) to find the equation:
y - (-3) = (3/5)(x - 6)
y + 3 = (3/5)(x - 6)
Therefore, the correct equation that represents the line passing through the points is:
y + 3 = (3/5)(x - 6)