SOLUTION: Write a linear equation in the form y=mx+b givien the following information. b) has a slope of 2/3 and passes through the point (12,3). c) passes through the points (5,5) (-3,-

Algebra ->  Linear-equations -> SOLUTION: Write a linear equation in the form y=mx+b givien the following information. b) has a slope of 2/3 and passes through the point (12,3). c) passes through the points (5,5) (-3,-      Log On


   

Question 175495: Write a linear equation in the form y=mx+b givien the following information.
b) has a slope of 2/3 and passes through the point (12,3).
c) passes through the points (5,5) (-3,-1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
b)



If you want to find the equation of line with a given a slope of 2%2F3 which goes through the point (12,3), 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=%282%2F3%29%28x-12%29 Plug in m=2%2F3, x%5B1%5D=12, and y%5B1%5D=3 (these values are given)


y-3=%282%2F3%29x%2B%282%2F3%29%28-12%29 Distribute 2%2F3

y-3=%282%2F3%29x-8 Multiply 2%2F3 and -12 to get -8

y=%282%2F3%29x-8%2B3 Add 3 to both sides to isolate y

y=%282%2F3%29x-5 Combine like terms -8 and 3 to get -5
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Answer:


So the equation of the line with a slope of 2%2F3 which goes through the point (12,3) is:

y=%282%2F3%29x-5 which is now in y=mx%2Bb form where the slope is m=2%2F3 and the y-intercept is b=-5

Notice if we graph the equation y=%282%2F3%29x-5 and plot the point (12,3), we get (note: if you need help with graphing, check out this solver)

Graph of y=%282%2F3%29x-5 through the point (12,3)
and we can see that the point lies on the line. Since we know the equation has a slope of 2%2F3 and goes through the point (12,3), this verifies our answer.







c)




First let's find the slope of the line through the points and


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


m=%28-1-5%29%2F%28-3-5%29 Plug in y%5B2%5D=-1, y%5B1%5D=5, x%5B2%5D=-3, and x%5B1%5D=5


m=%28-6%29%2F%28-3-5%29 Subtract 5 from -1 to get -6


m=%28-6%29%2F%28-8%29 Subtract 5 from -3 to get -8


m=3%2F4 Reduce


So the slope of the line that goes through the points and is m=3%2F4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-5=%283%2F4%29%28x-5%29 Plug in m=3%2F4, x%5B1%5D=5, and y%5B1%5D=5


y-5=%283%2F4%29x%2B%283%2F4%29%28-5%29 Distribute


y-5=%283%2F4%29x-15%2F4 Multiply


y=%283%2F4%29x-15%2F4%2B5 Add 5 to both sides.


y=%283%2F4%29x%2B5%2F4 Combine like terms. note: If you need help with fractions, check out this solver.


y=%283%2F4%29x%2B5%2F4 Simplify


So the equation that goes through the points and is y=%283%2F4%29x%2B5%2F4


Notice how the graph of y=%283%2F4%29x%2B5%2F4 goes through the points and . So this visually verifies our answer.
Graph of y=%283%2F4%29x%2B5%2F4 through the points and