Line j has an equation of y-8=-(2)/(3)(x+5). Line k is perpendicular to line j and passes through (-6,-2). What is the equation of line k ?

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Line  j has an equation of  y-8=-(2)/(3)(x+5). Line  k is perpendicular to line  j and passes through  (-6,-2). What is the equation of line  k ?

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Convert to Slope-Intercept Form: Convert the equation of line j to slope-intercept form to find its slope. The equation of line j is given as y - 8 = -(2/3)(x + 5). To convert it to slope-intercept form (y = mx + b), we need to isolate y on one side of the equation. y - 8 = -(2/3)(x + 5) y = -(2/3)(x + 5) + 8 y = -(2/3)x - (2/3)(5) + 8 y = -(2/3)x - 10/3 + 24/3 y = -(2/3)x + 14/3 The slope (m) of line j is -2/3.Determine Perpendicular Slope: Determine the slope of line k, which is perpendicular to line j. Since line k is perpendicular to line j, its slope will be the negative reciprocal of the slope of line j. The slope of line j is -2/3, so the negative reciprocal is 3/2. Therefore, the slope (m) of line k is 3/2.Use Point-Slope Form: Use the point-slope form to find the equation of line k. Line k passes through the point (-6, -2) and has a slope of 3/2. The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the slope and the point (-6, -2), we get: y - (-2) = (3/2)(x - (-6)) y + 2 = (3/2)(x + 6)Simplify to Slope-Intercept Form: Simplify the equation of line k to slope-intercept form. y + 2 = (3/2)(x + 6) y + 2 = (3/2)x + (3/2)(6) y + 2 = (3/2)x + 9 Subtract 2 from both sides to isolate y: y = (3/2)x + 9 - 2 y = (3/2)x + 7 The equation of line k in slope-intercept form is y = (3/2)x + 7.

Line $j$ has an equation of $y-8=-\frac{2}{3}(x+5)$ . Line $k$ is perpendicular to line $j$ and passes through $(-6,-2)$ . What is the equation of line $k$ ?

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Line $j$ has an equation of $y-8=-\frac{2}{3}(x+5)$ . Line $k$ is perpendicular to line $j$ and passes through $(-6,-2)$ . What is the equation of line $k$ ?