A direct variation always goes through the origin of the coordinate plane. TrueFalse
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Answer:
The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( -2 , 7)
To Find:
Equation of Line that passes through the point (-2,7) and is perpendicular to the line x-6y=42=?
Solution:
..................Given
which can be written as
Where m is the slope of the line
∴
On Comparing we get
The Required line is Perpendicular to the above line.
So,
Product of slopes = - 1
Slope of the required line is -6
Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,
i.e equation in point - slope form
Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2, 7) and slope = -6 we get
The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is
Recall that over an appropriate domain,
Let and
(these belong to the "appropriate domain", so the identity holds). We have
and
Then the sum telescopes, as