SOLUTION: I need your help with this problem: Determine a relationship between the x and y values. Write an equation. If X is 1,2,3,4. And Y is -6,-5,-4,and -3.

Algebra ->  Linear-equations -> SOLUTION: I need your help with this problem: Determine a relationship between the x and y values. Write an equation. If X is 1,2,3,4. And Y is -6,-5,-4,and -3.       Log On


   

Question 110439: I need your help with this problem: Determine a relationship between the x and y values. Write an equation. If X is 1,2,3,4. And Y is -6,-5,-4,and -3. If you do reply to me I greatly appriciate it for I have a test tomorro and I don't understand this question. I hope I wrote the question to where you can understand it easily. Thanks again for all your help!
Found 2 solutions by checkley71, edjones:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
x-y=d where d=difference
1-(-6)=d
1+6=d
d=7 which is the difference.
2-(-5)=d
2+5=7
3-(-4)=d
3+4=7

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(1,-6)(4,-3)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,-6) and (4,-3)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (1,-6) and (x%5B2%5D,y%5B2%5D) is the second point (4,-3))


m=%28-3--6%29%2F%284-1%29 Plug in y%5B2%5D=-3,y%5B1%5D=-6,x%5B2%5D=4,x%5B1%5D=1 (these are the coordinates of given points)


m=+3%2F3 Subtract the terms in the numerator -3--6 to get 3. Subtract the terms in the denominator 4-1 to get 3




m=1 Reduce



So the slope is

m=1





------------------------------------------------


Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y--6=%281%29%28x-1%29 Plug in m=1, x%5B1%5D=1, and y%5B1%5D=-6 (these values are given)



y%2B6=%281%29%28x-1%29 Rewrite y--6 as y%2B6



y%2B6=1x%2B%281%29%28-1%29 Distribute 1


y%2B6=1x-1 Multiply 1 and -1 to get -1%2F1. Now reduce -1%2F1 to get -1

y=1x-1-6 Subtract 6 from both sides to isolate y


y=1x-7 Combine like terms -1 and -6 to get -7

------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (1,-6) and (4,-3) is:y=1x-7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1 and the y-intercept is b=-7


Notice if we graph the equation y=1x-7 and plot the points (1,-6) and (4,-3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=1x-7 through the points (1,-6) and (4,-3)


Notice how the two points lie on the line. This graphically verifies our answer.