SOLUTION: find the slope-intercept equation of the line passing through (2,1)with a slope 0f m = 3.

Algebra ->  Graphs -> SOLUTION: find the slope-intercept equation of the line passing through (2,1)with a slope 0f m = 3.       Log On


   

Question 142365This question is from textbook
: find the slope-intercept equation of the line passing through (2,1)with a slope 0f m = 3. This question is from textbook

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 (2,1), 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 is the given point

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

y-1=%283%29%28x-2%29 Plug in m=3, x%5B1%5D=2, and y%5B1%5D=1 (these values are given)


y-1=3x%2B%283%29%28-2%29 Distribute 3

y-1=3x-6 Multiply 3 and -2 to get -6

y=3x-6%2B1 Add 1 to both sides to isolate y

y=3x-5 Combine like terms -6 and 1 to get -5
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Answer:


So the equation of the line with a slope of 3 which goes through the point (2,1) is:

y=3x-5 which is now in y=mx%2Bb form where the slope is m=3 and the y-intercept is b=-5

Notice if we graph the equation y=3x-5 and plot the point (2,1), we get (note: if you need help with graphing, check out this solver)

Graph of y=3x-5 through the point (2,1)
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 (2,1), this verifies our answer.