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The equation 6-2y=x is graphed in the xy-plane. Which of the following is a true statement about the graph? Choose 1 answer: (A) The graph's x-intercept is 6 and its y-intercept is -2 . B The graph's x-intercept is 6 and its y-intercept is 2 . (C) The graph has a slope of -2 . (D) The graph has a slope of -(1)/(2).

The equation 6−2y=x 6-2 y=x is graphed in the xy x y -plane. Which of the following is a true statement about the graph?\newlineChoose 11 answer:\newline(A) The graph's x x -intercept is 66 and its y y -intercept is −2-2 .\newlineB The graph's x x -intercept is 66 and its y y -intercept is 22 .\newline(C) The graph has a slope of −2-2 .\newline(D) The graph has a slope of −12 -\frac{1}{2} .

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Q. The equation 6−2y=x 6-2 y=x is graphed in the xy x y -plane. Which of the following is a true statement about the graph?\newlineChoose 11 answer:\newline(A) The graph's x x -intercept is 66 and its y y -intercept is −2-2 .\newlineB The graph's x x -intercept is 66 and its y y -intercept is 22 .\newline(C) The graph has a slope of −2-2 .\newline(D) The graph has a slope of −12 -\frac{1}{2} .
  1. Convert Equation to Slope-Intercept Form: Convert the given equation to slope-intercept form.\newlineThe slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. To convert the given equation 6−2y=x6 - 2y = x to this form, we need to solve for yy.
  2. Isolate y in Equation: Isolate y on one side of the equation.\newlineStarting with 6−2y=x6 - 2y = x, we can subtract 66 from both sides to get −2y=x−6-2y = x - 6.
  3. Divide by −2-2 to Solve: Divide both sides by −2-2 to solve for yy. Dividing both sides by −2-2 gives us y=−(12)x+3y = -\left(\frac{1}{2}\right)x + 3.
  4. Identify Slope and Y-Intercept: Identify the slope and y-intercept from the equation.\newlineFrom the equation y=−(12)x+3y = -(\frac{1}{2})x + 3, we can see that the slope (mm) is −12-\frac{1}{2} and the y-intercept (bb) is 33.
  5. Determine X-Intercept: Determine the x-intercept.\newlineTo find the x-intercept, we set yy to 00 and solve for xx. Plugging y=0y = 0 into the equation gives us 0=−(12)x+30 = -\left(\frac{1}{2}\right)x + 3. Solving for xx, we get x=6x = 6.
  6. Evaluate Answer Choices: Evaluate the answer choices.\newline(A) The graph's xx-intercept is 66 and its yy-intercept is −2-2. (Incorrect, the yy-intercept is 33)\newline(B) The graph's xx-intercept is 66 and its yy-intercept is 22. (Incorrect, the yy-intercept is 33)\newline(C) The graph has a slope of −2-2. (Incorrect, the slope is 6633)\newline(D) The graph has a slope of 6633. (Correct, as determined in Step 44)

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