Question Watch Video Show Examples If 2x=-1+y-xy then find the equations of all tangent lines to the curve when y=-5. Answer Attempt 1 out of 2

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Question Watch Video Show Examples If  2x=-1+y-xy then find the equations of all tangent lines to the curve when  y=-5. Answer Attempt 1 out of 2

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Differentiate Equation: First, we need to find the derivative of the given equation with respect to x to find the slope of the tangent line at any point (x, y) on the curve. The given equation is 2x = -1 + y - xy. To find the derivative, we will implicitly differentiate both sides of the equation with respect to x. d/dx (2x) = d/dx (-1 + y - xy) 2 = 0 + dy/dx - (y * d/dx (x) + x * d/dx (y)) 2 = dy/dx - y - x * dy/dx Now, we solve for dy/dx to find the slope of the tangent line. dy/dx (1 + x) = 2 + y dy/dx = (2 + y) / (1 + x)Substitute y = -5: Next, we substitute y = -5 into the derivative to find the slope of the tangent line at the points where y = -5. dy/dx = (2 + (-5)) / (1 + x) dy/dx = (-3) / (1 + x)Find x-coordinate: Now, we need to find the x-coordinates of the points on the curve where y = -5. We substitute y = -5 into the original equation to find x. 2x = -1 + (-5) - (-5)x 2x = -6 + 5x 3x = -6 x = -6 / 3 x = -2Find Specific Slope: We substitute x = -2 into the derivative to find the specific slope of the tangent line at the point where y = -5. dy/dx = (-3) / (1 + (-2)) dy/dx = (-3) / (-1) dy/dx = 3Equation of Tangent Line: Now that we have the slope of the tangent line and a point on the curve (x = -2, y = -5), we can use the point-slope form of the equation of a line to find the equation of the tangent line. The point-slope form is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Using the point (-2, -5) and the slope 3, the equation of the tangent line is: y - (-5) = 3(x - (-2)) y + 5 = 3(x + 2)Simplify Tangent Line: Finally, we simplify the equation of the tangent line to put it in slope-intercept form (y = mx + b). y + 5 = 3x + 6 y = 3x + 6 - 5 y = 3x + 1 This is the equation of the tangent line to the curve at the point where y = -5.

If $2x = -1 + y - xy$ then find the equations of all tangent lines to the curve when $y = -5.$

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If 2x=−1+y−xy2x = -1 + y - xy2x=−1+y−xy then find the equations of all tangent lines to the curve when y=−5.y = -5.y=−5.

If $2x = -1 + y - xy$ then find the equations of all tangent lines to the curve when $y = -5.$