Answer :
The equation of the required line is y = (2/3)x + 1
For given question,
We need to find an equation of the line passing through the point (-3, -1) and perpendicular to the line y = (-3/2)x - 4
Let m1 be the slope of required line and m2 be the slope of the line y = (-3/2)x - 4
so, m2 = -3/2
As required line is perpendicular to the line y = (-3/2)x - 4
⇒ m1 × m2 = -1
⇒ m1 × (-3/2) = -1
⇒ m1 = 2/3
So, the slope of the required line is 2/3.
Let (x1, y1) = (-3, -1)
Using slope-point form of the line, the required equation of the line would be,
⇒ (y - y1) = m(x - x1)
⇒ (y - (-1)) = 2/3 (x - (-3))
⇒ y + 1 = 2/3 (x + 3)
⇒ y + 1 = 2/3 x + 2
⇒ y = (2/3)x + 2 - 1
⇒ y = (2/3)x + 1
Therefore, the equation of the required line is y = (2/3)x + 1
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