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Which of the following equations represents a line that passes through the points (3,-11) and (6,-20) ? I. 6x+2y=-2 II. y+21=-3(x-6) Neither I only II only I and II

Which of the following equations represents a line that passes through the points (3,−11) (3,-11) and (6,−20) (6,-20) ?\newlineI. 6x+2y=−2 6 x+2 y=-2 \newlineII. y+21=−3(x−6) y+21=-3(x-6) \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 (3,−11) (3,-11) and (6,−20) (6,-20) ?\newlineI. 6x+2y=−2 6 x+2 y=-2 \newlineII. y+21=−3(x−6) y+21=-3(x-6) \newlineNeither\newlineI only\newlineII only\newlineI and II
  1. Calculate Point-Slope Form: Now that we have the slope, we can use one of the points and the slope to write the equation of the line in point-slope form, which is y−y1=m(x−x1)y - y_1 = m(x - x_1). Let's use the point (3,−11)(3,-11) and the slope −3-3. y−(−11)=−3(x−3)y - (-11) = -3(x - 3) y+11=−3x+9y + 11 = -3x + 9 Now, let's move everything to one side to get the standard form of the line, Ax+By=CAx + By = C. y=−3x+9−11y = -3x + 9 - 11 y=−3x−2y = -3x - 2 So, the standard form is 3x+y=−23x + y = -2.
  2. Check Equation I: We need to check if either of the given equations matches the equation we found.\newlineLet's start with equation I: 6x+2y=−26x + 2y = -2.\newlineTo compare it with our equation, we can divide everything by 22 to simplify it.\newline(6x+2y)/2=−2/2(6x + 2y) / 2 = -2 / 2\newline3x+y=−13x + y = -1\newlineThis equation does not match our equation 3x+y=−23x + y = -2, so equation I is not correct.
  3. Check Equation II: Now let's check equation II: y+21=−3(x−6)y + 21 = -3(x - 6). We can distribute the −3-3 and move everything to one side to get the standard form. y+21=−3x+18y + 21 = -3x + 18 y=−3x+18−21y = -3x + 18 - 21 y=−3x−3y = -3x - 3 This equation does not match our equation 3x+y=−23x + y = -2 either, so equation II is not correct.
  4. Final Answer: Since neither equation II nor equation IIII matches the equation we derived from the points (3,−11)(3,-11) and (6,−20)(6,-20), the correct answer is ＂Neither.＂

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