SOLUTION: write an equation of a line that passes through each point with the given slope (3,7),m = -3

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Question 115121This question is from textbook Algebra 1
: write an equation of a line that passes through each point with the given slope
(3,7),m = -3 This question is from textbook Algebra 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 -3 which goes through the point (3,7), 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-7=%28-3%29%28x-3%29 Plug in m=-3, x%5B1%5D=3, and y%5B1%5D=7 (these values are given)


y-7=-3x%2B%28-3%29%28-3%29 Distribute -3

y-7=-3x%2B9 Multiply -3 and -3 to get 9

y=-3x%2B9%2B7 Add 7 to both sides to isolate y

y=-3x%2B16 Combine like terms 9 and 7 to get 16
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Answer:


So the equation of the line with a slope of -3 which goes through the point (3,7) is:

y=-3x%2B16 which is now in y=mx%2Bb form where the slope is m=-3 and the y-intercept is b=16

Notice if we graph the equation y=-3x%2B16 and plot the point (3,7), we get (note: if you need help with graphing, check out this solver)

Graph of y=-3x%2B16 through the point (3,7)
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 (3,7), this verifies our answer.