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Write the standard form of the equation of the line passing through the point (1,2) and perpendicular to the line x-5y=10

User Juude
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1 Answer

6 votes

Answer:

5x + y = 7

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange x - 5y = 10 into this form

Subtract x from both sides

- 5y = - x + 10 ( divide all terms by - 5 )

y =
(1)/(5) x - 2 ← in point- slope form

with 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, thus

y = - 5x + c ← is the partial equation of the line

To find c substitute (1, 2) into the partial equation

2 = - 5 + c ⇒ c = 2 + 5 = 7

y = - 5x + 7 ← in slope - intercept form

Add 5x to both sides

5x + y = 7 ← in standard form

User Aarbor
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