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Which of the following is an equation of the line in the xy plane with x-intercept -(2)/(7) and y intercept (8)/(7) ? Choose 1 answer: (A) 7y-28 x=8 (B) 7y+28 x=8 (C) -7y+28 x=8 (D) -7y-28 x=8

Which of the following is an equation of the line in the xy x y plane with x x -intercept −27 -\frac{2}{7} and y y intercept 87 \frac{8}{7} ?\newlineChoose 11 answer:\newline(A) 7y−28x=8 7 y-28 x=8 \newline(B) 7y+28x=8 7 y+28 x=8 \newline(C) −7y+28x=8 -7 y+28 x=8 \newline(D) −7y−28x=8 -7 y-28 x=8

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Q. Which of the following is an equation of the line in the xy x y plane with x x -intercept −27 -\frac{2}{7} and y y intercept 87 \frac{8}{7} ?\newlineChoose 11 answer:\newline(A) 7y−28x=8 7 y-28 x=8 \newline(B) 7y+28x=8 7 y+28 x=8 \newline(C) −7y+28x=8 -7 y+28 x=8 \newline(D) −7y−28x=8 -7 y-28 x=8
  1. Intercept form of line equation: To find the equation of the line, we can use the intercept form of a line's equation, which is xa+yb=1\frac{x}{a} + \frac{y}{b} = 1, where aa is the xx-intercept and bb is the yy-intercept.
  2. Substituting x-intercept and y-intercept: Given the x-intercept is −27-\frac{2}{7} and the y-intercept is 87\frac{8}{7}, we substitute these values into the intercept form equation: x−(27)+y(87)=1\frac{x}{-\left(\frac{2}{7}\right)} + \frac{y}{\left(\frac{8}{7}\right)} = 1.
  3. Clearing the fractions: To clear the fractions, we multiply every term by the least common denominator, which in this case is 77: 7×(x−(27))+7×(y87)=7×17\times\left(\frac{x}{-\left(\frac{2}{7}\right)}\right) + 7\times\left(\frac{y}{\frac{8}{7}}\right) = 7\times 1.
  4. Simplifying the equation: Simplifying the equation, we get −7×(x−(27))+7×(y87)=7-7\times\left(\frac{x}{-\left(\frac{2}{7}\right)}\right) + 7\times\left(\frac{y}{\frac{8}{7}}\right) = 7, which simplifies to 7x−2+7y8=7\frac{7x}{-2} + \frac{7y}{8} = 7.
  5. Multiplying to clear fractions: Multiplying through by the denominators to clear the fractions gives us (7x×(−72))+(7y×(78))=7×7(7x \times (-\frac{7}{2})) + (7y \times (\frac{7}{8})) = 7 \times 7.
  6. Getting rid of fractions: Simplifying the equation, we get −492×x+498×y=49-\frac{49}{2} \times x + \frac{49}{8} \times y = 49.
  7. Multiplying to simplify: To get rid of the fractions, we can multiply the entire equation by the least common multiple of the denominators, which is 88: 8×(−492×x)+8×(498×y)=8×498\times\left(-\frac{49}{2} \times x\right) + 8\times\left(\frac{49}{8} \times y\right) = 8\times49.
  8. Dividing to simplify: Simplifying the equation, we get −4×49×x+49×y=8×49-4 \times 49 \times x + 49 \times y = 8 \times 49.
  9. Rearranging to standard form: This simplifies to −196x+49y=392-196x + 49y = 392.
  10. Matching the answer choices: Dividing the entire equation by 4949 to simplify it further, we get −4x+y=8-4x + y = 8.
  11. Checking our work: Finally, we rearrange the equation to match the standard form Ax+By=CAx + By = C, which gives us y+4x=8y + 4x = 8.
  12. Checking our work: Finally, we rearrange the equation to match the standard form Ax+By=CAx + By = C, which gives us y+4x=8y + 4x = 8. Multiplying the entire equation by 77 to match the answer choices, we get 7y+28x=567y + 28x = 56.
  13. Checking our work: Finally, we rearrange the equation to match the standard form Ax+By=CAx + By = C, which gives us y+4x=8y + 4x = 8. Multiplying the entire equation by 77 to match the answer choices, we get 7y+28x=567y + 28x = 56. We notice that none of the answer choices match the equation 7y+28x=567y + 28x = 56. We must have made a mistake in our calculations. Let's go back and check our work.

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