SOLUTION: graph the line with slope 4 passing through the point (4,2)

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Question 124709: graph the line with slope 4 passing through the point (4,2)
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 4 which goes through the point (4,2), 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-2=%284%29%28x-4%29 Plug in m=4, x%5B1%5D=4, and y%5B1%5D=2 (these values are given)


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

y-2=4x-16 Multiply 4 and -4 to get -16

y=4x-16%2B2 Add 2 to both sides to isolate y

y=4x-14 Combine like terms -16 and 2 to get -14
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Answer:


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

y=4x-14 which is now in y=mx%2Bb form where the slope is m=4 and the y-intercept is b=-14

Notice if we graph the equation y=4x-14 and plot the point (4,2), we get (note: if you need help with graphing, check out this solver)

Graph of y=4x-14 through the point (4,2)
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 (4,2), this verifies our answer.