Question 637712: ``Please help!
Determine the slope of the line through each pair of points.
1)parallel to the line y= -2x+3 containing the point (-2, -1)
Thankyou!' step by step please
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Problem: Derive the equation of the line that is parallel to the line y = -2*x + 3, and passes through the point (-2,-1).
The first property that we must learn about this problem is "What makes two lines parallel?" (Please refer to your text to read about parallel lines.) Two or more lines are parallel if and only if their SLOPES are the same (equal). How do you know the slope of a line?
Step 1) Arrange your equation into the form y = m*x + b, where m and b represent constants
Step 2) What is the coefficient of x from step 1)
Step 3) The slope of your line is called m (why m? I don't know), it is equal to the coefficient of step 2)
Apply these steps to your problem
Step 1) y = -2*x + 3; If it was not given in this form you should rearrange it.
Step 2) the coefficient of x is (-2)
Step 3) m = -2
This is the required slope of the line parallel to the given line. Now we need to make the line pass through the point (-2,-1). There are two methods of doing this. The first method is to perform the following step;
1) Slope m = -2
2) Point is (x1,y1) = (-2, -1)
3) General formula (y-y1) = m*(x-x1)
y -(-1) = -2*(x-(-2))
y + 1 = -2x -4
y = -2x -5 is the equation of the line parallel to the given line, passing through the point (-2,-1).
The second method (by DrBeeee) -
1) Slope is m = -2
2) Point is (x1,y1) = (-2,-1)
3) The general formula y1 = m*x1 +b
-1 = -2*(-2) + b
b = -1 -4
b = -5
y = -2x -5 is the equation of the line parallel to the given line, passing through the point (-2,-1).
Either method works - take your pick.
Comment: The method(s) given above are used to find the equation of a line when you are given the slope and a point.
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