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 pointslope form. (1,2) , m = 1/2 y  y1 = m(x  x1) {pointslope form} y  2 = (1/2)(x  1) {substituted point and slope into pointslope 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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