SOLUTION: Write the equation of the line that passes through point (–7, –15) with a slope of 3.

Algebra ->  Coordinate-system -> SOLUTION: Write the equation of the line that passes through point (–7, –15) with a slope of 3.       Log On


   

Question 113889: Write the equation of the line that passes through point (–7, –15) with a slope of 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 3 which goes through the point (-7,-15), 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--15=%283%29%28x--7%29 Plug in m=3, x%5B1%5D=-7, and y%5B1%5D=-15 (these values are given)


y%2B15=%283%29%28x--7%29 Rewrite y--15 as y%2B15


y%2B15=%283%29%28x%2B7%29 Rewrite x--7 as x%2B7


y%2B15=3x%2B%283%29%287%29 Distribute 3

y%2B15=3x%2B21 Multiply 3 and 7 to get 21

y=3x%2B21-15 Subtract 15 from both sides to isolate y

y=3x%2B6 Combine like terms 21 and -15 to get 6
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Answer:


So the equation of the line with a slope of 3 which goes through the point (-7,-15) is:

y=3x%2B6 which is now in y=mx%2Bb form where the slope is m=3 and the y-intercept is b=6

Notice if we graph the equation y=3x%2B6 and plot the point (-7,-15), we get (note: if you need help with graphing, check out this solver)

Graph of y=3x%2B6 through the point (-7,-15)
and we can see that the point lies on the line. Since we know the equation has a slope of 3 and goes through the point (-7,-15), this verifies our answer.