SOLUTION: help me to write an equation in slope-intercept form, containing the given point and having the given slope. (-3,-2);m=5/2

Algebra ->  Graphs -> SOLUTION: help me to write an equation in slope-intercept form, containing the given point and having the given slope. (-3,-2);m=5/2      Log On


   

Question 115116: help me to write an equation in slope-intercept form, containing the given point and having the given slope.
(-3,-2);m=5/2
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 5%2F2 which goes through the point (-3,-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=%285%2F2%29%28x--3%29 Plug in m=5%2F2, x%5B1%5D=-3, and y%5B1%5D=-2 (these values are given)


y%2B2=%285%2F2%29%28x--3%29 Rewrite y--2 as y%2B2


y%2B2=%285%2F2%29%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B2=%285%2F2%29x%2B%285%2F2%29%283%29 Distribute 5%2F2

y%2B2=%285%2F2%29x%2B15%2F2 Multiply 5%2F2 and 3 to get 15%2F2

y=%285%2F2%29x%2B15%2F2-2 Subtract 2 from both sides to isolate y

y=%285%2F2%29x%2B11%2F2 Combine like terms 15%2F2 and -2 to get 11%2F2 (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 5%2F2 which goes through the point (-3,-2) is:

y=%285%2F2%29x%2B11%2F2 which is now in y=mx%2Bb form where the slope is m=5%2F2 and the y-intercept is b=11%2F2

Notice if we graph the equation y=%285%2F2%29x%2B11%2F2 and plot the point (-3,-2), we get (note: if you need help with graphing, check out this solver)

Graph of y=%285%2F2%29x%2B11%2F2 through the point (-3,-2)
and we can see that the point lies on the line. Since we know the equation has a slope of 5%2F2 and goes through the point (-3,-2), this verifies our answer.