SOLUTION: write an equation of a line with the given slope and passes through the given point. m=-3;(1,4)

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Question 307178: write an equation of a line with the given slope and passes through the given point.
m=-3;(1,4)
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 -3 which goes through the point (1,4), 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-4=%28-3%29%28x-1%29 Plug in m=-3, x%5B1%5D=1, and y%5B1%5D=4 (these values are given)


y-4=-3x%2B%28-3%29%28-1%29 Distribute -3


y-4=-3x%2B3 Multiply -3 and -1 to get 3


y=-3x%2B3%2B4 Add 4 to both sides to isolate y


y=-3x%2B7 Combine like terms 3 and 4 to get 7

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Answer:


So the equation of the line with a slope of -3 which goes through the point (1,4) is y=-3x%2B7 which is now in y=mx%2Bb form where the slope is m=-3 and the y-intercept is b=7


Notice if we graph the equation y=-3x%2B7 and plot the point (1,4), we get (note: if you need help with graphing, check out this solver)

Graph of y=-3x%2B7 through the point (1,4)
and we can see that the point lies on the line. Since we know the equation has a slope of -3 and goes through the point (1,4), this verifies our answer.