SOLUTION: find an equation of the line that passes through the point (4,5) and has slope -2.

Algebra ->  Linear-equations -> SOLUTION: find an equation of the line that passes through the point (4,5) and has slope -2.      Log On


   

Question 117386: find an equation of the line that passes through the point (4,5) and has slope -2.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of -2 which goes through the point (4,5), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-5=%28-2%29%28x-4%29 Plug in m=-2, x%5B1%5D=4, and y%5B1%5D=5 (these values are given)


y-5=-2x%2B%28-2%29%28-4%29 Distribute -2

y-5=-2x%2B8 Multiply -2 and -4 to get 8

y=-2x%2B8%2B5 Add 5 to both sides to isolate y

y=-2x%2B13 Combine like terms 8 and 5 to get 13
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Answer:


So the equation of the line with a slope of -2 which goes through the point (4,5) is:

y=-2x%2B13 which is now in y=mx%2Bb form where the slope is m=-2 and the y-intercept is b=13

Notice if we graph the equation y=-2x%2B13 and plot the point (4,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=-2x%2B13 through the point (4,5)
and we can see that the point lies on the line. Since we know the equation has a slope of -2 and goes through the point (4,5), this verifies our answer.