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

User Rdworth
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1 Answer

6 votes

Answer:

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

User Ftnilsson
by
8.3k points

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