Question

A line is passing through point (-3,6) and (7,x)is perpendicular to 2x-10y=18.Find the value of x

Answer 1

x = - 44

Explanation:

the equation of a line in slope- intercept form is

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

given

2x - 10y = 18 ( subtract 2x from both sides )

- 10y = - 2x + 18 ( divide through by - 10 )

y =
`(-2)/(-10)` x +
`(18)/(-10)` , that is

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

with slope m =
`(1)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(5) )` = - 5

calculate the slope of the line through the 2 given points and equate to - 5

calculate slope m using slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, 6 ) and (x₂, y₂ ) = (7, x )

m =
`(x-6)/(7-(-3))` =
`(x-6)/(7+3)` =
`(x-6)/(10)`

then equating

`(x-6)/(10)` = - 5 ( multiply both sides by 10 to clear the fraction )

x - 6 = - 50 ( add 6 to both sides )

x = - 44