SOLUTION: Hello, I need help with two problems. 1. Find the slope of the line containing the given pair of points. If the slope is undefined state so (5,3) and (8,-4) 2. Select the line

Algebra ->  Algebra  -> Graphs -> SOLUTION: Hello, I need help with two problems. 1. Find the slope of the line containing the given pair of points. If the slope is undefined state so (5,3) and (8,-4) 2. Select the line       Log On

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Question 243697: Hello, I need help with two problems.
1. Find the slope of the line containing the given pair of points. If the slope is undefined state so (5,3) and (8,-4)
2. Select the line that has the given slope and y intercept. slope -1/5, y intercept (0,-2)
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Note: is the first point . So this means that x%5B1%5D=5 and y%5B1%5D=3.
Also, is the second point . So this means that x%5B2%5D=8 and y%5B2%5D=-4.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-4-3%29%2F%288-5%29 Plug in y%5B2%5D=-4, y%5B1%5D=3, x%5B2%5D=8, and x%5B1%5D=5


m=%28-7%29%2F%288-5%29 Subtract 3 from -4 to get -7


m=%28-7%29%2F%283%29 Subtract 5 from 8 to get 3


So the slope of the line that goes through the points and is m=-7%2F3




# 2

If you want to find the equation of line with a given a slope of -1%2F5 which goes through the point (0,-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=%28-1%2F5%29%28x-0%29 Plug in m=-1%2F5, x%5B1%5D=0, and y%5B1%5D=-2 (these values are given)


y%2B2=%28-1%2F5%29%28x-0%29 Rewrite y--2 as y%2B2


y%2B2=%28-1%2F5%29x%2B%28-1%2F5%29%28-0%29 Distribute -1%2F5


y%2B2=%28-1%2F5%29x%2B0 Multiply -1%2F5 and -0 to get 0


y=%28-1%2F5%29x%2B0-2 Subtract 2 from both sides to isolate y


y=%28-1%2F5%29x-2 Combine like terms
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Answer:


So the equation of the line with a slope of -1%2F5 which goes through the point (0,-2) is:

y=%28-1%2F5%29x-2 which is now in y=mx%2Bb form where the slope is m=-1%2F5 and the y-intercept is b=-2

Notice if we graph the equation y=%28-1%2F5%29x-2 and plot the point (0,-2), we get (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F5%29x-2 through the point (0,-2)

And we can see that the point lies on the line. Since we know the equation has a slope of -1%2F5 and goes through the point (0,-2), this verifies our answer.

Answer by stanbon(57203) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find the slope of the line containing the given pair of points. If the slope is undefined state so (5,3) and (8,-4)
---
slope = (-4-3)/(8-5) = -7/3
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2. Select the line that has the given slope and y intercept.
slope -1/5, y intercept (0,-2)
You have the slope and intercept. Put them into the form:
y = mx + b where m is the slope and b is the intercept.
Equation:
y = (-1/5)x-2
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Cheers,
Stan H.