SOLUTION: Find the equation of the line that contains the point (-3,5) and has the slope 2/3 A. y=2/3x-7 B. y=2/3x+5 C. y=2/3x+2 D. y=2/3x+7

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line that contains the point (-3,5) and has the slope 2/3 A. y=2/3x-7 B. y=2/3x+5 C. y=2/3x+2 D. y=2/3x+7       Log On


   

Question 169805: Find the equation of the line that contains the point (-3,5) and has the slope 2/3
A. y=2/3x-7
B. y=2/3x+5
C. y=2/3x+2
D. y=2/3x+7
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 (-3,5), 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-5=%282%2F3%29%28x--3%29 Plug in m=2%2F3, x%5B1%5D=-3, and y%5B1%5D=5 (these values are given)


y-5=%282%2F3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-5=%282%2F3%29x%2B%282%2F3%29%283%29 Distribute 2%2F3

y-5=%282%2F3%29x%2B2 Multiply 2%2F3 and 3 to get 2

y=%282%2F3%29x%2B2%2B5 Add 5 to both sides to isolate y

y=%282%2F3%29x%2B7 Combine like terms 2 and 5 to get 7
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Answer:


So the equation of the line with a slope of 2%2F3 which goes through the point (-3,5) is:

y=%282%2F3%29x%2B7 which is now in y=mx%2Bb form where the slope is m=2%2F3 and the y-intercept is b=7

Notice if we graph the equation y=%282%2F3%29x%2B7 and plot the point (-3,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%282%2F3%29x%2B7 through the point (-3,5)
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 (-3,5), this verifies our answer.