SOLUTION: If the slop of a line is 4/5 and the y-intercept is 3, what is the linear equation in the slop-intercept form?

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Question 120829: If the slop of a line is 4/5 and the y-intercept is 3, what is the linear equation in the slop-intercept form?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the y-intercept is 3, then the line goes through the point (0,3)




If you want to find the equation of line with a given a slope of 4%2F5 which goes through the point (0,3), 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=%284%2F5%29%28x-0%29 Plug in m=4%2F5, x%5B1%5D=0, and y%5B1%5D=3 (these values are given)


y-3=%284%2F5%29x%2B%284%2F5%29%28-0%29 Distribute 4%2F5

y-3=%284%2F5%29x%2B0 Multiply 4%2F5 and -0 to get 0

y=%284%2F5%29x%2B0%2B3 Add 3 to both sides to isolate y

y=%284%2F5%29x%2B3 Combine like terms 0 and 3 to get 3
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Answer:


So the equation of the line with a slope of 4%2F5 which goes through the point (0,3) is:

y=%284%2F5%29x%2B3 which is now in y=mx%2Bb form where the slope is m=4%2F5 and the y-intercept is b=3

Notice if we graph the equation y=%284%2F5%29x%2B3 and plot the point (0,3), we get (note: if you need help with graphing, check out this solver)

Graph of y=%284%2F5%29x%2B3 through the point (0,3)
and we can see that the point lies on the line. Since we know the equation has a slope of 4%2F5 and goes through the point (0,3), this verifies our answer.