Which of the following is an equation of the line in the xy-plane that passes through the point (-5,3) and is perpendicular to the line with equation y=-(1)/(8)x+6 ? Choose 1 answer: (A) y=-(1)/(8)x+43 (B) y=8x+43 (C) y=-(1)/(8)x-43 (D) y=8x-43

Question

Which of the following is an equation of the line in the  xy-plane that passes through the point  (-5,3) and is perpendicular to the line with equation  y=-(1)/(8)x+6 ? Choose 1 answer: (A)  y=-(1)/(8)x+43 (B)  y=8x+43 (C)  y=-(1)/(8)x-43 (D)  y=8x-43

Bytelearn · Accepted Answer

Determine slope of given line: Determine the slope of the given line. The equation of the given line is y=-(1)/(8)x+6. The slope of this line is the coefficient of x, which is -(1)/(8).Find perpendicular slope: Find the slope of the line that is perpendicular to the given line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The negative reciprocal of -(1)/(8) is 8.Write equation using point-slope form: Use the point-slope form to write the equation of the line. The point-slope form of the equation of a line is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We have the point (-5,3) and the slope 8. Plugging these values into the point-slope form gives us (y - 3) = 8(x - (-5)).Simplify to slope-intercept form: Simplify the equation from the point-slope form to the slope-intercept form. Simplifying (y - 3) = 8(x + 5) gives us y - 3 = 8x + 40. To get the slope-intercept form, we solve for y: y = 8x + 40 + 3, which simplifies to y = 8x + 43.Match equation to answer choice: Match the equation to the correct answer choice. The equation we found is y = 8x + 43, which corresponds to answer choice (B).

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