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Which of the following equations represents a line that passes through the points (0,6) and (10,0) ? I. y=(3)/(5)x+6 II. 3x+5y=35 Neither I only II only I and II

Which of the following equations represents a line that passes through the points (0,6) (0,6) and (10,0) (10,0) ?\newlineI. y=35x+6 y=\frac{3}{5} x+6 \newlineII. 3x+5y=35 3 x+5 y=35 \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 (0,6) (0,6) and (10,0) (10,0) ?\newlineI. y=35x+6 y=\frac{3}{5} x+6 \newlineII. 3x+5y=35 3 x+5 y=35 \newlineNeither\newlineI only\newlineII only\newlineI and II
  1. Calculate slope: Find the slope of the line passing through the points (0,6)(0,6) and (10,0)(10,0). The slope mm is calculated using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Here, (x1,y1)=(0,6)(x_1, y_1) = (0, 6) and (x2,y2)=(10,0)(x_2, y_2) = (10, 0). m=0−610−0=−610=−35m = \frac{0 - 6}{10 - 0} = \frac{-6}{10} = \frac{-3}{5}.
  2. Write equation in slope-intercept form: Use the slope and one of the points to write the equation of the line in slope-intercept form y=mx+by = mx + b.\newlineWe already have the slope m=−35m = -\frac{3}{5}, and we can use the point (0,6)(0,6) where x=0x = 0 and y=6y = 6.\newlineThe y-intercept bb is the y-value when x=0x = 0, which is 66.\newlineSo the equation of the line is y=(−35)x+6y = (-\frac{3}{5})x + 6.
  3. Check equation I: Check if equation I, y=35x+6y = \frac{3}{5}x + 6, matches the derived equation.\newlineThe derived equation is y=−35x+6y = \frac{-3}{5}x + 6, which is not the same as y=35x+6y = \frac{3}{5}x + 6.\newlineTherefore, equation I does not represent the line that passes through the points (0,6)(0,6) and (10,0)(10,0).
  4. Check equation II: Check if equation II, 3x+5y=353x + 5y = 35, can be the equation of the line.\newlineWe can rewrite equation II in slope-intercept form by solving for yy.\newline5y=−3x+355y = -3x + 35\newliney=−35x+7y = \frac{-3}{5}x + 7\newlineThis equation has the same slope as the derived equation but a different yy-intercept.\newlineTherefore, equation II does not represent the line that passes through the points (0,6)(0,6) and (10,0)(10,0).
  5. Determine correct answer: Determine the correct answer based on the checks in steps 33 and 44. Neither equation II nor equation IIII represents the line that passes through the given points. The correct answer is ＂Neither.＂

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