SOLUTION: Draw the line that has the given slope and passes through the given point. slope= -2/7; (-4,5)

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Question 127008: Draw the line that has the given slope and passes through the given point.
slope= -2/7; (-4,5)
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%2F7 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%2F7%29%28x--4%29 Plug in m=-2%2F7, x%5B1%5D=-4, and y%5B1%5D=5 (these values are given)


y-5=%28-2%2F7%29%28x%2B4%29 Rewrite x--4 as x%2B4


y-5=%28-2%2F7%29x%2B%28-2%2F7%29%284%29 Distribute -2%2F7

y-5=%28-2%2F7%29x-8%2F7 Multiply -2%2F7 and 4 to get -8%2F7

y=%28-2%2F7%29x-8%2F7%2B5 Add 5 to both sides to isolate y

y=%28-2%2F7%29x%2B27%2F7 Combine like terms -8%2F7 and 5 to get 27%2F7 (note: if you need help with combining fractions, check out this solver)


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Answer:


So the equation of the line with a slope of -2%2F7 which goes through the point (-4,5) is:

y=%28-2%2F7%29x%2B27%2F7 which is now in y=mx%2Bb form where the slope is m=-2%2F7 and the y-intercept is b=27%2F7

Notice if we graph the equation y=%28-2%2F7%29x%2B27%2F7 and plot the point (-4,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-2%2F7%29x%2B27%2F7 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%2F7 and goes through the point (-4,5), this verifies our answer.