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

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*