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Write the equation of the line that passes through the points (-1,6) and (-3,-6). 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 (−1,6) (-1,6) and (−3,−6) (-3,-6) . 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 (−1,6) (-1,6) and (−3,−6) (-3,-6) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate slope using formula: Calculate the slope (mm) of the line using the formula m=(y2−y1)(x2−x1)m = \frac{(y_2 - y_1)}{(x_2 - x_1)}. We have the points (−1,6)(-1,6) and (−3,−6)(-3,-6), so let's plug these into the formula: m=(−6−6)(−3−(−1))=(−12)(−2)=6m = \frac{(-6 - 6)}{(-3 - (-1))} = \frac{(-12)}{(-2)} = 6.
  2. Use point-slope form: Use the point-slope form of the equation of a line, which is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineWe can use either of the two points for (x1,y1)(x_1, y_1). Let's use the first point (−1,6)(-1,6).
  3. Substitute slope and point: Substitute the slope mm and the point (−1,6)(-1,6) into the point-slope form equation.y−6=6(x−(−1))y - 6 = 6(x - (-1)) simplifies to y−6=6(x+1)y - 6 = 6(x + 1).
  4. Check for simplification: Check the equation for any possible simplification.\newlineThe equation y−6=6(x+1)y - 6 = 6(x + 1) is already in the simplest point-slope form, so no further simplification is needed.

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