Question

Write an equation of a line in STANDARD FORM that passes through the point (7,10) and is PERPENDICULAR to the line x-2y=18

Answer 1

2x + y = 24

Explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

The first step is to obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

given the line with equation

x - 2y = 18 ( subtract x from both sides )

- 2y = - x + 18 ( divide through by - 2 )

`(-2)/(-2)` y =
`(-1)/(-2)` x +
`(18)/(-2)` , that is

y =
`(1)/(2)` x - 9 ← in slope- intercept form

with slope m =
`(1)/(2)`

given a line with slope m, then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(2) )` = - 2 , then

y = - 2x + c ← is the partial equation

to find c , substitute (7, 10 ) for x and y in the partial equation

10 = - 2(7) + c = - 14 + c ( add 14 to both sides )

24 = c

y = - 2x + 24 ← equation in slope- intercept form

add 2x to both sides

2x + y = 24 ← equation in standard form