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It is VERY EASY.
The given line x + 2y = -4 has the slope m = .
You MOMENTARILY find it (the slope) by transforming the given equation to the form y = .
Next, the perpendicular line has the slope, which is reciprocal opposite to , i.e. 2.
Thus the perpendicular line has the form
y = 2x + c. (1)
The constant term "c" in this equation is now UNKNOWN, but we momentarily will find it using the condition
that the given point (-3,-5) lies on the line (1).
For it, substitute coordinates x= -3 and y= -5 into equation (1). You will get
-5 = 2*(-3) + c,
which gives you c = - 5 + 6 = 1.
So, your final equation is y = 2x + 1. ANSWER
Solved.
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For this and many other similar problems see the lessons
- Find the slope of a straight line in a coordinate plane passing through two given points
- Equation for a straight line having a given slope and passing through a given point
- Solving problems related to the slope of a straight line
- Equation for a straight line in a coordinate plane passing through two given points
- Equation for a straight line parallel to a given line and passing through a given point
- Equation for a straight line perpendicular to a given line and passing through a given point (*)
in this site.
The most relevant of them is the lesson marked (*) in the list.
Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.