SOLUTION: What is an equation of a line passing through the point(-2,3) and having a slope of 4? thanks for your help.

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Question 202034: What is an equation of a line passing through the point(-2,3) and having a slope of 4? thanks for your help.
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 (-2,3), 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%29%28x--2%29 Plug in m=4, x%5B1%5D=-2, and y%5B1%5D=3 (these values are given)


y-3=%284%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-3=4x%2B%284%29%282%29 Distribute 4

y-3=4x%2B8 Multiply 4 and 2 to get 8

y=4x%2B8%2B3 Add 3 to both sides to isolate y

y=4x%2B11 Combine like terms 8 and 3 to get 11
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Answer:


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

y=4x%2B11 which is now in y=mx%2Bb form where the slope is m=4 and the y-intercept is b=11

Notice if we graph the equation y=4x%2B11 and plot the point (-2,3), we get (note: if you need help with graphing, check out this solver)

Graph of y=4x%2B11 through the point (-2,3)
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 (-2,3), this verifies our answer.