SOLUTION: Find the equation of the line that contains the point (2,-3) and has slope 2/3 A. y=2/3x-13/3 B. y=2/3x+5/3 C. y=-2/3x-13/3 D. y=-2/3x-5/3

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line that contains the point (2,-3) and has slope 2/3 A. y=2/3x-13/3 B. y=2/3x+5/3 C. y=-2/3x-13/3 D. y=-2/3x-5/3      Log On


   

Question 169825: Find the equation of the line that contains the point (2,-3) and has slope 2/3
A. y=2/3x-13/3
B. y=2/3x+5/3
C. y=-2/3x-13/3
D. y=-2/3x-5/3
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 2%2F3 which goes through the point (2,-3), 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--3=%282%2F3%29%28x-2%29 Plug in m=2%2F3, x%5B1%5D=2, and y%5B1%5D=-3 (these values are given)


y%2B3=%282%2F3%29%28x-2%29 Rewrite y--3 as y%2B3


y%2B3=%282%2F3%29x%2B%282%2F3%29%28-2%29 Distribute 2%2F3


y%2B3=%282%2F3%29x-4%2F3 Multiply 2%2F3 and -2 to get -4%2F3


y=%282%2F3%29x-4%2F3-3 Subtract 3 from both sides to isolate y


y=%282%2F3%29x-13%2F3 Combine like terms -4%2F3 and -3 to get -13%2F3 (note: if you need help with combining fractions, check out this solver)


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Answer:


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

y=%282%2F3%29x-13%2F3 which is now in y=mx%2Bb form where the slope is m=2%2F3 and the y-intercept is b=-13%2F3

Notice if we graph the equation y=%282%2F3%29x-13%2F3 and plot the point (2,-3), we get (note: if you need help with graphing, check out this solver)

Graph of y=%282%2F3%29x-13%2F3 through the point (2,-3)
and we can see that the point lies on the line. Since we know the equation has a slope of 2%2F3 and goes through the point (2,-3), this verifies our answer.