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Find the x-intercept of the line that passes through (-3,4) and is perpendicular to the graph of x-2y=7

User Anirban Sarkar
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1 Answer

11 votes
11 votes

Answer:

x - intercept = - 1

Explanation:

the equation of a line in slope- intercept form is

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

given

x - 2y = 7 ( subtract x from both sides )

- 2y = - x + 7 ( divide through by - 2 )

y =
(1)/(2) x +
(7)/(2) ← 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 of the perpendicular line\to find c substitute (- 3, 4 ) into the partial equation

4 = 6 + c ⇒ c = 4 - 6 = - 2

y = - 2x - 2 ← equation of perpendicular line

to find the x- intercept let y = 0 into the equation and solve for x

- 2x - 2 = 0 ( add 2 to both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

the x- intercept of the perpendicular line is - 1 or (- 1, 0 )

User ErikHeemskerk
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3.1k points