SOLUTION: Write the equation of each line. Give the answer in slope-intercept form. The line through (-1,-2)with slope of 3/7 The answer is y=3/7x-11/7 How do I work this problem t

Algebra ->  Linear-equations -> SOLUTION: Write the equation of each line. Give the answer in slope-intercept form. The line through (-1,-2)with slope of 3/7 The answer is y=3/7x-11/7 How do I work this problem t      Log On


   

Question 118003: Write the equation of each line. Give the answer in slope-intercept form.
The line through (-1,-2)with slope of 3/7
The answer is y=3/7x-11/7
How do I work this problem to get that answer?
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%2F7 which goes through the point (-1,-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=%283%2F7%29%28x--1%29 Plug in m=3%2F7, x%5B1%5D=-1, and y%5B1%5D=-2 (these values are given)


y%2B2=%283%2F7%29%28x--1%29 Rewrite y--2 as y%2B2


y%2B2=%283%2F7%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B2=%283%2F7%29x%2B%283%2F7%29%281%29 Distribute 3%2F7

y%2B2=%283%2F7%29x%2B3%2F7 Multiply 3%2F7 and 1 to get 3%2F7

y=%283%2F7%29x%2B3%2F7-2 Subtract 2 from both sides to isolate y

y=%283%2F7%29x-11%2F7 Combine like terms 3%2F7 and -2 to get -11%2F7 (note: if you need help with combining fractions, check out this solver)


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Answer:


So the equation of the line with a slope of 3%2F7 which goes through the point (-1,-2) is:

y=%283%2F7%29x-11%2F7 which is now in y=mx%2Bb form where the slope is m=3%2F7 and the y-intercept is b=-11%2F7

Notice if we graph the equation y=%283%2F7%29x-11%2F7 and plot the point (-1,-2), we get (note: if you need help with graphing, check out this solver)

Graph of y=%283%2F7%29x-11%2F7 through the point (-1,-2)
and we can see that the point lies on the line. Since we know the equation has a slope of 3%2F7 and goes through the point (-1,-2), this verifies our answer.