The line m goes through the points (1, 2) and (5, 10). Which of the following is the equation of a line perpendicular to m and passing through the point (1,2) ?
A.) 4x + 2y = 6 B.) 2x - y = 0 C.) x + y = 3 D.) x + 2y = 6 E.) x + 2y = 5 Perpendicular lines have slopes which are negative reciprocals.Find the slope of the line passing through the two given points. (1,2) and (5,10) {the two given points} y2 - y1 --------- = slope {slope formula} x2 - x1 10 - 2 --------- = slope {substituted coordinates into slope formula} 5 - 1 8 --- = slope {subtracted on top and bottom} 4 slope = 2 {divided} perpendicular slope is -1/2 {perpendicular lines have slopes which are negative reciprocals} Substitute the coordinates of the point, (1,2), along with the slope, -1/2, into point-slope form. (1,2) , m = -1/2 y - y1 = m(x - x1) {point-slope form} y - 2 = (-1/2)(x - 1) {substituted point and slope into point-slope form} -2y + 4 = x - 1 {multiplied entire equation by -2, to eliminate fraction} x + 2y = 5 {added 2y and added 1 to each side}E.)- Algebra House
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