The equation 6y+12 x=18 is graphed in the xy-plane. Which of the following equations has a graph that is perpendicular to the graph of the given equation? Choose 1 answer: (A) y=-2x+3 (B) y=(1)/(2)x+3 (C) y=2x+3 (D) y=-(1)/(2)x+3

Question

The equation  6y+12 x=18 is graphed in the  xy-plane. Which of the following equations has a graph that is perpendicular to the graph of the given equation? Choose 1 answer: (A)  y=-2x+3 (B)  y=(1)/(2)x+3 (C)  y=2x+3 (D)  y=-(1)/(2)x+3

Bytelearn · Accepted Answer

Find slope of line: Find the slope of the given line. The equation of the given line is 6y + 12x = 18. To find the slope, we need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope.Rewrite equation in slope-intercept form: Rewrite the given equation in slope-intercept form. Starting with 6y + 12x = 18, we subtract 12x from both sides to get 6y = -12x + 18. Then, we divide each term by 6 to solve for y, which gives us y = -2x + 3. The slope of this line is -2.Determine slope of perpendicular line: Determine the slope of the line that is perpendicular to the given line. The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line. Since the slope of the given line is -2, the negative reciprocal is 1/2.Identify equation with negative reciprocal slope: Identify the equation with the slope that is the negative reciprocal of the given line's slope. We are looking for an equation with a slope of 1/2. Among the options given: (A) y = -2x + 3 has a slope of -2. (B) y = (1/2)x + 3 has a slope of 1/2. (C) y = 2x + 3 has a slope of 2. (D) y = -(1/2)x + 3 has a slope of -1/2. The correct equation is the one with the slope of 1/2, which is option (B).

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