Which of the following is an equation of the line in the xy plane with x-intercept (5)/(3) and y intercept (10)/(7) ? Choose 1 answer: (A) -7y+6x=10 (B) 7y+6x=-10 (c) 7y+6x=10 (D) 7y-6x=10

Question

Which of the following is an equation of the line in the  xy plane with  x-intercept  (5)/(3) and  y intercept  (10)/(7) ? Choose 1 answer: (A)  -7y+6x=10 (B)  7y+6x=-10 (c)  7y+6x=10 (D)  7y-6x=10

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Finding Intercepts: The x-intercept of a line is the point where the line crosses the x-axis, which means the y-coordinate is 0. Similarly, the y-intercept is where the line crosses the y-axis, meaning the x-coordinate is 0. We can use these intercepts to find the equation of the line in the form of Ax + By = C, where A, B, and C are constants.Substituting x-intercept: Given the x-intercept (5/3, 0), we can substitute x = 5/3 and y = 0 into the equation Ax + By = C to find the relationship between A and C. A(5/3) + B(0) = C 5A/3 = CSubstituting y-intercept: Given the y-intercept (0, 10/7), we can substitute x = 0 and y = 10/7 into the equation Ax + By = C to find the relationship between B and C. A(0) + B(10/7) = C 10B/7 = CEquating the expressions for C: We now have two equations relating A, B, and C: 5A/3 = C 10B/7 = C We can equate these two expressions for C to find the relationship between A and B. 5A/3 = 10B/7 Multiplying both sides by 21 (the least common multiple of 3 and 7) to clear the fractions, we get: 35A = 30BSolving for A and B: To find A and B, we can choose a common multiple of 35 and 30 that will make A and B integers. The smallest such number is 210, so we can set 35A = 210 and 30B = 210. Solving for A and B gives us: A = 210/35 = 6 B = 210/30 = 7Solving for C: Now that we have A and B, we can use either of the two equations we found earlier to solve for C: 5A/3 = C 5(6)/3 = C C = 10Final Equation: We have found A = 6, B = 7, and C = 10. The equation of the line is therefore: 6x + 7y = 10Comparing with answer choices: We can now compare the equation we found with the answer choices given: (A) -7y + 6x = 10 (B) 7y + 6x = -10 (C) 7y + 6x = 10 (D) 7y - 6x = 10 The correct equation that matches our derived equation is (C) 7y + 6x = 10.

Which of the following is an equation of the line in the $x y$ plane with $x$ -intercept $\frac{5}{3}$ and $y$ intercept $\frac{10}{7}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-7 y+6 x=10$ $\newline$ (B) $7 y+6 x=-10$ $\newline$ (C) $7 y+6 x=10$ $\newline$ (D) $7 y-6 x=10$

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