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Determine the equation of the line passing through (-2, -4) and (-8, -64).

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Final answer:

The equation of the line passing through (-2, -4) and (-8, -64) is y = 10x + 16.

Step-by-step explanation:

The equation of the line passing through (-2, -4) and (-8, -64) can be found using the slope-intercept form of a linear equation, which is y = mx + b. To find the slope (m), we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the values (-2, -4) and (-8, -64) into the formula, we get m = (-64 - (-4)) / (-8 - (-2)) = -60 / -6 = 10.

Now that we have the slope, we can substitute it into the slope-intercept form to find the y-intercept (b). Using the point (-2, -4), we have -4 = 10(-2) + b, which simplifies to -4 = -20 + b. Solving for b gives us b = 16.

Therefore, the equation of the line is y = 10x + 16.

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