Which of the following is true of the graph of (y)/(9)-(x)/(6)=1 in the xy-plane? Choose 1 answer: (A) The graph's x-intercept is -6 and its y-intercept is 9 . (B) The graph's x-intercept is 9 and its y-intercept is -6 . (c) The graph is a line with a slope of (2)/(3). (D) The graph is a line with a slope of -(3)/(2).

Question

Which of the following is true of the graph of  (y)/(9)-(x)/(6)=1 in the  xy-plane? Choose 1 answer: (A) The graph's  x-intercept is -6 and its  y-intercept is 9 . (B) The graph's  x-intercept is 9 and its  y-intercept is -6 . (c) The graph is a line with a slope of  (2)/(3). (D) The graph is a line with a slope of  -(3)/(2).

Bytelearn · Accepted Answer

Finding the x-intercept: To find the x-intercept, we set y to 0 and solve for x. (y)/(9)-(x)/(6)=1 Substitute y = 0: (0)/(9)-(x)/(6)=1 Simplify: -x/6 = 1 Multiply both sides by -6 to solve for x: x = -6Finding the y-intercept: To find the y-intercept, we set x to 0 and solve for y. (y)/(9)-(x)/(6)=1 Substitute x = 0: (y)/(9)-(0)/(6)=1 Simplify: y/9 = 1 Multiply both sides by 9 to solve for y: y = 9Finding the slope of the graph: To find the slope of the graph, we need to rewrite the equation in slope-intercept form (y = mx + b). (y)/(9)-(x)/(6)=1 Multiply everything by the least common multiple of 9 and 6, which is 18, to clear the fractions: 18*(y/9) - 18*(x/6) = 18*1 Simplify: 2y - 3x = 18 Rearrange to solve for y: 2y = 3x + 18 Divide everything by 2: y = (3/2)x + 9 The slope of the graph is the coefficient of x, which is 3/2.

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