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Which of the following equations represents a line that passes through the points (4,-16) and (0,-4) ? I. 6x+2y=-6 II. y=3x-4 Neither I only II only I and II

Which of the following equations represents a line that passes through the points (4,−16) (4,-16) and (0,−4) (0,-4) ?\newlineI. 6x+2y=−6 6 x+2 y=-6 \newlineII. y=3x−4 y=3 x-4 \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 (4,−16) (4,-16) and (0,−4) (0,-4) ?\newlineI. 6x+2y=−6 6 x+2 y=-6 \newlineII. y=3x−4 y=3 x-4 \newlineNeither\newlineI only\newlineII only\newlineI and II
  1. Calculate slope: Use the two points to find the slope of the line.\newlineThe slope mm is calculated using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.\newlineUsing the points (4,−16)(4, -16) and (0,−4)(0, -4), we get:\newlinem=−4−(−16)0−4=12−4=−3m = \frac{-4 - (-16)}{0 - 4} = \frac{12}{-4} = -3.
  2. Write point-slope 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 (0,−4)(0, -4) and the slope −3-3 to write the equation:\newliney−(−4)=−3(x−0)y - (-4) = -3(x - 0)\newlineSimplifying, we get:\newliney+4=−3xy + 4 = -3x\newliney=−3x−4y = -3x - 4
  3. Check Equation I: Check if Equation I 6x+2y=−66x + 2y = -6 represents the line.\newlineTo check if the line passes through the points 4,−164, -16 and 0,−40, -4, we can plug these points into the equation and see if they satisfy it.\newlineFor point 4,−164, -16:\newline6(4)+2(−16)=24−32=−86(4) + 2(-16) = 24 - 32 = -8, which is not equal to (-6\).\newlineTherefore, Equation I does not represent the line.
  4. Check Equation II: Check if Equation II y=3x−4y = 3x - 4 represents the line.\newlineWe already found that the equation of the line is y=−3x−4y = -3x - 4.\newlineEquation II is y=3x−4y = 3x - 4, which has a slope of 33, not −3-3.\newlineTherefore, Equation II does not represent the line either.
  5. Determine correct answer: Determine the correct answer based on the checks from Steps 33 and 44. Since neither Equation II nor Equation IIII represents the line that passes through the points (4,−16)(4, -16) and (0,−4)(0, -4), the correct answer is ＂Neither.＂

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