SOLUTION: Write an equation of the line that passes through the given point and has the given slope (3,1), m+4

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Question 92330: Write an equation of the line that passes through the given point and has the given slope
(3,1), m+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming it suppose to look like "m=4" not "m+4"




If you want to find the equation of line with a given a slope of 4 which goes through the point (3,1), 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 (x%5B1%5D,y%5B1%5D) is the given point

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

y-1=%284%29%28x-3%29 Plug in m=4, x%5B1%5D=3, and y%5B1%5D=1 (these values are given)

y-1=%284%29x-%284%29%283%29%29 Distribute 4


y-1=%284%29x-12 Multiply -4 and 3 to get -12

y=%284%29x-12%2B1Add 1 to both sides

y=4x-11 Combine like terms
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Answer:


So the equation of the line with a slope of 4 which goes through the point (3,1) is:

y=4x-11 which is now in y=mx%2Bb form where the slope is m=4 and the y-intercept is b=-11

Notice if we graph the equation y=4x-11 and plot the point (3,1), we get (note: if you need help with graphing, check out this solver)

Graph of y=4x-11 through the point (3,1)
and we can see that the point lies on the line. Since we know the equation has a slope of 4 and goes through the point (3,1), this verifies our answer.