find the perpendicular line equation?

Question

Write an equation of the line containing the given point and perpendicular to the given point.(7,9);2x+y=6?

Answer 1

The line of the equation :2x + y = 6

The slope m = -(x-coeficient) / (y-coeficient)

m = -2 / 1

m = -2

The perpendiculer slope : 1 / 2 (The product of the two slopes is -1)

The point is (7 , 9)

The perpendicular line of the equation :y - y1 = m(x - x1)

Substitute m = 1 / 2 and x1 =7 , y1 = 9 in the above equation

y - 9 =1 / 2( x - 7)

Multiply each side by 2

2y - 18 = x - 7

Add 18 to each side

2y - 18 + 18 = x - 7 + 18

2y = x + 11

Subtract 2y from each side

x - 2y + 11 = 0

or

y = x / 2 + 11 / 2.

 

Answer 2

 

2x+y=6 ------> y = -2x + 6

compare it with slope intercept form line equation y = mx + c . m = slope.

m = -2

the lines are perpendicular so new line slope = -1/m = 1/2

the line equation in point slope form is y - y1 = m (x - x1)

y - 9 = 1/2 ( x -7)

2y - 18 = x - 7

x -2y = -11