SOLUTION: Find the equation of the line. Slope -1/3 y-intercept (0,3/2) The problem is I do not know how to begin solving it could you give me the steps or an example of this problem

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line. Slope -1/3 y-intercept (0,3/2) The problem is I do not know how to begin solving it could you give me the steps or an example of this problem       Log On


   

Question 87244: Find the equation of the line.
Slope -1/3 y-intercept (0,3/2)
The problem is I do not know how to begin solving it could you give me the steps or an example of this problem with using same method but different numbers.
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 -1%2F3 which goes through the point (0,3%2F2), 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-3%2F2=%28-1%2F3%29%28x-0%29 Plug in m=-1%2F3, x%5B1%5D=0, and y%5B1%5D=3%2F2 (these values are given)

y-3%2F2=%28-1%2F3%29x-%28-1%2F3%29%280%29%29 Distribute -1%2F3

y-3%2F2=%28-1%2F3%29x%2B%281%2F3%29%280%29%29 Multiply the negatives

y-3%2F2=%28-1%2F3%29x%2B0 Multiply 1%2F3 and 0 to get 0

y=%28-1%2F3%29x%2B0%2B3%2F2Add 3%2F2 to both sides

y=%28-1%2F3%29x%2B3%2F2 Combine like terms
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Answer:


So the equation of the line with a slope of -1%2F3 which goes through the point (0,3%2F2) is:

y=%28-1%2F3%29x%2B3%2F2 which is now in y=mx%2Bb form where the slope is m=-1%2F3 (so this shows our equation has a slope of -1%2F3) and the y-intercept is b=3%2F2

Notice if we graph the equation y=%28-1%2F3%29x%2B3%2F2 (note: if you need help with graphing, check out this solver) and plot the point (0,3%2F2), we get

Graph of y=%28-1%2F3%29x%2B3%2F2 through the point (0,3%2F2)
and we can see that the point lies on the line. Since we know the equation has a slope of -1%2F3 and goes through the point (0,3%2F2), this verifies our answer.