Equation of a line that is perpendicular {ACT}

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