SOLUTION: write the equation of the line which has a y-intercept of -4 and slope 5\3

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Question 118998: write the equation of the line which has a y-intercept of -4 and slope 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 5%2F3 which goes through the point (0,-4), 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--4=%285%2F3%29%28x-0%29 Plug in m=5%2F3, x%5B1%5D=0, and y%5B1%5D=-4 (these values are given)


y%2B4=%285%2F3%29%28x-0%29 Rewrite y--4 as y%2B4


y%2B4=%285%2F3%29x%2B%285%2F3%29%28-0%29 Distribute 5%2F3

y%2B4=%285%2F3%29x%2B0 Multiply 5%2F3 and -0 to get 0

y=%285%2F3%29x%2B0-4 Subtract 4 from both sides to isolate y

y=%285%2F3%29x-4 Combine like terms 0 and -4 to get -4
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Answer:


So the equation of the line with a slope of 5%2F3 which goes through the point (0,-4) is:

y=%285%2F3%29x-4 which is now in y=mx%2Bb form where the slope is m=5%2F3 and the y-intercept is b=-4

Notice if we graph the equation y=%285%2F3%29x-4 and plot the point (0,-4), we get (note: if you need help with graphing, check out this solver)

Graph of y=%285%2F3%29x-4 through the point (0,-4)
and we can see that the point lies on the line. Since we know the equation has a slope of 5%2F3 and goes through the point (0,-4), this verifies our answer.