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Which of the following equations represents a line that passes through the points (-2,-9) and (3,-4) ? I. y+9=(x+2) II. y=x-7 Neither I only II only I and II

Which of the following equations represents a line that passes through the points (−2,−9) (-2,-9) and (3,−4) (3,-4) ?\newlineI. y+9=(x+2) y+9=(x+2) \newlineII. y=x−7 y=x-7 \newlineNeither\newlineI only\newlineII only\newlineI and II

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Q. Which of the following equations represents a line that passes through the points (−2,−9) (-2,-9) and (3,−4) (3,-4) ?\newlineI. y+9=(x+2) y+9=(x+2) \newlineII. y=x−7 y=x-7 \newlineNeither\newlineI only\newlineII only\newlineI and II
  1. Calculate slope: Calculate the slope of the line passing through the points (−2,−9)(-2,-9) and (3,−4)(3,-4). The slope mm is given by the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points. m=−4−(−9)3−(−2)m = \frac{-4 - (-9)}{3 - (-2)} m=55m = \frac{5}{5} m=1m = 1
  2. Write equation: Use the slope and one of the points to write the equation of the line in point-slope form.\newlineWe can use the point (−2,−9)(-2,-9) and the slope m=1m = 1 to write the equation.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newliney−(−9)=1(x−(−2))y - (-9) = 1(x - (-2))\newliney+9=1(x+2)y + 9 = 1(x + 2)
  3. Check equation I: Check if equation I, y+9=(x+2)y+9=(x+2), matches the equation derived from the point-slope form.\newlineThe derived equation is y+9=1(x+2)y + 9 = 1(x + 2), which simplifies to y+9=x+2y + 9 = x + 2.\newlineEquation I is y+9=x+2y + 9 = x + 2, which is the same as the derived equation.\newlineTherefore, equation I is correct.
  4. Check equation II: Check if equation II, y=x−7y=x-7, is correct by plugging in the coordinates of the two points.\newlineFirst, plug in the point (−2,−9)(-2,-9):\newline−9=(−2)−7-9 = (-2) - 7\newline−9=−9-9 = -9\newlineThis point satisfies equation II.
  5. Verify both equations: Plug in the second point (3,−4)(3,-4) into equation II to verify if it also satisfies the equation.\newline−4=(3)−7-4 = (3) - 7\newline−4=−4-4 = -4\newlineThis point also satisfies equation II.
  6. Verify both equations: Plug in the second point (3,−4)(3,-4) into equation II to verify if it also satisfies the equation.\newline−4=(3)−7-4 = (3) - 7\newline−4=−4-4 = -4\newlineThis point also satisfies equation II.Since both points satisfy equation II, y=x−7y=x-7, and we have already confirmed that equation I is correct, both equations I and II represent the line that passes through the points (−2,−9)(-2,-9) and (3,−4)(3,-4).

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