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Which of the following equations represents a line that passes through the points (0,3) and (-10,-17) ? I. y-11=2(x-6) II. y=2x+5 Neither I only II only I and II

Which of the following equations represents a line that passes through the points (0,3) (0,3) and (−10,−17) (-10,-17) ?\newlineI. y−11=2(x−6) y-11=2(x-6) \newlineII. y=2x+5 y=2 x+5 \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 (0,3) (0,3) and (−10,−17) (-10,-17) ?\newlineI. y−11=2(x−6) y-11=2(x-6) \newlineII. y=2x+5 y=2 x+5 \newlineNeither\newlineI only\newlineII only\newlineI and II
  1. Calculate Slope: First, let's find the slope of the line that passes through the points (0,3)(0,3) and (−10,−17)(-10,-17). The slope mm is calculated using 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.\newlinem=−17−3−10−0m = \frac{-17 - 3}{-10 - 0}\newlinem=−20−10m = \frac{-20}{-10}\newlinem=2m = 2
  2. Find Equation: Now that we have the slope, we can 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), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line. We can use the point (0,3)(0,3) to find the equation of the line.y−3=2(x−0)y - 3 = 2(x - 0)y−3=2xy - 3 = 2xy=2x+3y = 2x + 3This is the equation of the line that passes through the points (0,3)(0,3) and (−10,−17)(-10,-17).
  3. Check Equation I: Let's check if equation I, y−11=2(x−6)y - 11 = 2(x - 6), represents the line that passes through the points (0,3)(0,3) and (−10,−17)(-10,-17). We can simplify this equation to see if it matches the equation we found.\newliney−11=2(x−6)y - 11 = 2(x - 6)\newliney=2x−12+11y = 2x - 12 + 11\newliney=2x−1y = 2x - 1\newlineThis equation does not match the equation y=2x+3y = 2x + 3 that we found, so equation I does not represent the line that passes through the given points.
  4. Check Equation II: Next, let's check if equation II, y=2x+5y = 2x + 5, represents the line that passes through the points (0,3)(0,3) and (−10,−17)(-10,-17). We compare this equation to the equation we found, y=2x+3y = 2x + 3. Since the equation y=2x+5y = 2x + 5 has a different y-intercept than the equation y=2x+3y = 2x + 3, equation II also does not represent the line that passes through the given points.
  5. Final Answer: Since neither equation I nor equation II matches the equation y=2x+3y = 2x + 3, which is the correct equation of the line that passes through the points (0,3)(0,3) and (−10,−17)(-10,-17), the correct answer is ＂Neither.＂

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