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

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) (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 which goes through the point (2,-3), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---

where is the slope, and

is the given point

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

Plug in , , and (these values are given)

Rewrite as

Distribute

Multiply and to get

Subtract 3 from both sides to isolate y

Combine like terms and to get (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 which goes through the point (,) is:

which is now in form where the slope is and the y-intercept is

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

Graph of 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 and goes through the point (,), this verifies our answer.
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