SOLUTION: Write an equation in point-slope form of the line containing the point (-4,-5) and parallel to the line 2x+y=-3.

Algebra ->  Algebra  -> Coordinate-system -> SOLUTION: Write an equation in point-slope form of the line containing the point (-4,-5) and parallel to the line 2x+y=-3.      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 180706: Write an equation in point-slope form of the line containing the point (-4,-5) and parallel to the line 2x+y=-3.
Answer by jim_thompson5910(14872) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2By=-3 Start with the given equation.


y=-3-2x Subtract 2x from both sides.


y=-2x-3 Rearrange the terms.


We can see that the equation y=-2x-3 has a slope m=-2 and a y-intercept b=-3.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-2.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-2 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--5=-2%28x--4%29 Plug in m=-2, x%5B1%5D=-4, and y%5B1%5D=-5


y--5=-2%28x%2B4%29 Rewrite x--4 as x%2B4


y%2B5=-2%28x%2B4%29 Rewrite y--5 as y%2B5


-------------------------------------------------

Answer:

So the equation of the line, in point-slope form, parallel to 2x%2By=-3 that goes through the point is y%2B5=-2%28x%2B4%29.


In short, the equation that you're looking for is y%2B5=-2%28x%2B4%29


Here's a graph to visually verify our answer:
drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-3-2x%29%2F1%2C-2%28x%2B4%29-5%29%2C%0D%0Acircle%28-4%2C-5%2C0.08%29%2C%0D%0Acircle%28-4%2C-5%2C0.10%29%2C%0D%0Acircle%28-4%2C-5%2C0.12%29%0D%0A%29Graph of the original equation 2x%2By=-3 (red) and the parallel line y%2B5=-2%28x%2B4%29 (green) through the point .