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Write the equation of the line that passes through the points (-1,-4) and (6,-8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line. Answer:

Write the equation of the line that passes through the points (−1,−4) (-1,-4) and (6,−8) (6,-8) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

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Q. Write the equation of the line that passes through the points (−1,−4) (-1,-4) and (6,−8) (6,-8) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate Slope: Find the slope of the line using the two given points.\newlineThe slope mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.\newlineUsing the points (−1,−4)(-1, -4) and (6,−8)(6, -8), we calculate the slope as follows:\newlinem=−8−(−4)6−(−1)m = \frac{-8 - (-4)}{6 - (-1)}\newlinem=−8+46+1m = \frac{-8 + 4}{6 + 1}\newlinem=−47m = \frac{-4}{7}
  2. Write Point-Slope Equation: Use one of the points and the slope to write the equation in point-slope form.\newlineThe point-slope form of the equation of a line is y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line.\newlineUsing the slope −47-\frac{4}{7} and the point (−1,−4)(-1, -4), the equation becomes:\newliney−(−4)=(−47)(x−(−1))y - (-4) = \left(-\frac{4}{7}\right)(x - (-1))\newliney+4=(−47)(x+1)y + 4 = \left(-\frac{4}{7}\right)(x + 1)
  3. Simplify Equation: Simplify the equation if necessary.\newlineIn this case, the equation is already in the correct form and does not need further simplification.

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