Question

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Answer 1

By comparing it with the standard equation : y = mx + c

We get the slope(m) as = - 1/3

Since the product of the slopes of perpendicular lines = - 1,

Slope of the perpendicular line = - 1/(-1/3)
= 3
The perpendicular line passes through the point (1,4) = (x, y)

Using slope point form:
y - y1 = m ( x - x1)

y - 4 = 3 ( x - 1)

y - 4 = 3x - 3

y = 3x + 1 ( option c)

Answer 2

We know that : If Two Lines are Perpendicular to each other, then Product of their Slopes should be Equal to -1

$Given\;Line : y = \frac{-1}{3}x - 2$

Comparing with Standard form : y = mx + c

We can notice that : Slope of the line is $= \frac{-1}{3}$

⇒ $\frac{-1}{3}\times Slope\;of\;Line\;Perpendicular = -1$

⇒ Slope of Line Perpendicular to the given line is 3

We know that the form of line passing through point (x₀ , y₀) and having slope m is : y - y₀ = m(x - x₀)

Here the line passes through the point (1 , 4)

⇒ x₀ = 1 and y₀ = 4

We found : Slope(m) = 3

Substituting all the values in the standard form, We get :

Equation of the line : y - 4 = 3(x - 1)

⇒ y - 4 = 3x - 3

⇒ y = 3x + 1