SOLUTION: Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line.

Algebra ->  Coordinate-system -> SOLUTION: Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line.      Log On


   

Question 113888: Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we have the y-intercept (0, –5), then the line goes through the point (0, –5)




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


y%2B5=%284%29%28x-0%29 Rewrite y--5 as y%2B5


y%2B5=4x%2B%284%29%28-0%29 Distribute 4

y%2B5=4x%2B0 Multiply 4 and -0 to get 0

y=4x%2B0-5 Subtract 5 from both sides to isolate y

y=4x-5 Combine like terms 0 and -5 to get -5
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Answer:


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

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

Notice if we graph the equation y=4x-5 and plot the point (0,-5), we get (note: if you need help with graphing, check out this solver)

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