SOLUTION: Graph the line with the given point and slope. The line through (-2, 5) with a slope -1.

Algebra ->  Graphs -> SOLUTION: Graph the line with the given point and slope. The line through (-2, 5) with a slope -1.      Log On


   

Question 176417: Graph the line with the given point and slope.
The line through (-2, 5) with a slope -1.
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 -1 which goes through the point (-2,5), 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=%28-1%29%28x--2%29 Plug in m=-1, x%5B1%5D=-2, and y%5B1%5D=5 (these values are given)


y-5=%28-1%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-5=-1x%2B%28-1%29%282%29 Distribute -1


y-5=-1x-2 Multiply -1 and 2 to get -2


y=-1x-2%2B5 Add 5 to both sides to isolate y


y=-1x%2B3 Combine like terms -2 and 5 to get 3


y=-x%2B3 Simplify
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Answer:


So the equation of the line with a slope of -1 which goes through the point (-2,5) is:

y=-x%2B3 which is now in y=mx%2Bb form where the slope is m=-1 and the y-intercept is b=3

Notice if we graph the equation y=-x%2B3 and plot the point (-2,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=-x%2B3 through the point (-2,5)
and we can see that the point lies on the line. Since we know the equation has a slope of -1 and goes through the point (-2,5), this verifies our answer.