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Question 113488: Find the equation in standard form. with all integer coefficients, of the line perpendicular to 3x - 6y and passing through (-2,-1).
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
First find the slope for the line 
the slope is:
…..solve for  ; move  to the right
 ….. divide both sides by 
 …..
 …..
=>…
Since the line which we are looking for is perpendicular to the line
, and we know that   have
   , then the slope of the line which
we are looking for is:
 ….this is a slope of the line which we are looking for
We also know that the line which we are looking for passing through (-2,-1)
Now, we can find equation of a line   and   . Here is solution:
| Solved by pluggable solver: FIND a line by slope and one point |
What we know about the line whose equation we are trying to find out:
- it goes through point (-2, -1)
- it has a slope of -2
First, let's draw a diagram of the coordinate system with point (-2, -1) plotted with a little blue dot:
Write this down: the formula for the equation, given point  and intercept a, is
 (see a paragraph below explaining why this formula is correct)
Given that a=-2, and  , we have the equation of the line:
Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point ( ,  ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out:  . So, then, the equation of the line is:  .
Here's the graph:
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the equation in standard form is:
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