Find the equation of the line perpendicular to the line (3x - 2y = 6) and passing through the point ((2,-1)).

Question

Accepted Answer

Step:1 ：First, we rewrite the given line in slope-intercept form ((y = mx + b)). This gives us (y = frac{3}{2}x - 3).Step:2 ：The slope of a line perpendicular to a line with slope (m) is (-frac{1}{m}). Thus, the slope of the line we are trying to find is (-frac{2}{3}).Step:3 ：Finally, we use the point-slope form of the equation of a line ((y - y_1 = m(x - x_1))) to find the equation of the line. Plugging in the given point ((2,-1)) and the slope (-frac{2}{3}), we get (y + 1 = -frac{2}{3}(x - 2)).Step:4 ：Simplifying this equation gives us the final equation of the line in slope-intercept form: (y = -frac{2}{3}x + frac{1}{3}).

Answer

Step: 1 ：First, we rewrite the given line in slope-intercept form ((y = mx + b)). This gives us (y = frac{3}{2}x - 3).Step: 2 ：The slope of a line perpendicular to a line with slope (m) is (-frac{1}{m}). Thus, the slope of the line we are trying to find is (-frac{2}{3}).Step: 3 ：Finally, we use the point-slope form of the equation of a line ((y - y_1 = m(x - x_1))) to find the equation of the line. Plugging in the given point ((2,-1)) and the slope (-frac{2}{3}), we get (y + 1 = -frac{2}{3}(x - 2)).Step: 4 ：Simplifying this equation gives us the final equation of the line in slope-intercept form: (y = -frac{2}{3}x + frac{1}{3}).

Find the equation of the line perpendicular to the line $3 x - 2 y = 6$ and passing through the point $(2, - 1)$ .

Answer

Popular Problems

Find the equation of the line perpendicular to the line 3x−2y=6 and passing through the point (2,−1).

Answer

Popular Problems

Find the equation of the line perpendicular to the line $3 x - 2 y = 6$ and passing through the point $(2, - 1)$ .