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Write the equation of the line that passes through the points (-3,1) and (0,-3). 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 (−3,1) (-3,1) and (0,−3) (0,-3) . 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 (−3,1) (-3,1) and (0,−3) (0,-3) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate Slope: Calculate the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Given points: (−3,1)(-3,1) and (0,−3)(0,-3). Let's use (x1,y1)=(−3,1)(x_1, y_1) = (-3, 1) and (x2,y2)=(0,−3)(x_2, y_2) = (0, -3). m=−3−10−(−3)=−43=−43m = \frac{-3 - 1}{0 - (-3)} = \frac{-4}{3} = -\frac{4}{3}.
  2. Point-Slope Form: Use the point-slope form of the equation of a line: 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 point (−3,1)(-3, 1).\newlinePoint-slope form: y−1=(−43)(x−(−3))y - 1 = \left(-\frac{4}{3}\right)(x - (-3)).
  3. Simplify Equation: Simplify the equation.\newliney−1=(−43)(x+3)y - 1 = \left(-\frac{4}{3}\right)(x + 3).\newlineNow distribute the slope −43-\frac{4}{3} across (x+3)(x + 3).\newliney−1=(−43)x−(43)⋅3y - 1 = \left(-\frac{4}{3}\right)x - \left(\frac{4}{3}\right)\cdot 3.\newliney−1=(−43)x−4y - 1 = \left(-\frac{4}{3}\right)x - 4.
  4. Check Equation: Check if the equation is fully simplified and in the correct form.\newlineThe equation y−1=(−43)x−4y - 1 = \left(-\frac{4}{3}\right)x - 4 is in point-slope form and is fully simplified.

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