Write the equation of the line in standard form

Question

Through (-4,7); perpendicular to x-2y=0

Answer 1

Perpendicular lines have slopes that are negative reciprocals of each other. So, rearrange that equation into slope-intercept form (y=mx+b) to find the perpendicular line's slope:

 

x - 2y = 0

x = 2y

(1/2)x = y

 

The negative reciprocal of 1/2 is -2. So, your line's slope is -2.

 

 

Write your line's equation in point-slope form using slope m = -2 and point (x₁, y₁) = (-4, 7):

 

y - y₁ = m(x - x₁)

y - 7 = -2(x + 4)

 

 

Rearrange that equation into standard form (Ax + By = C) by getting x and y together on one side:

 

y = -2(x + 4) + 7

y = -2x - 8 + 7

2x + y = -8 + 7

2x + y = -1