SOLUTION: Hi My name is Kaleea I have to write a Linear Equation Given Two Points step 1: find the slope step 2: use the two point snd slope in Point-Slope

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Question 135826: Hi My name is Kaleea
I have to write a Linear Equation Given Two Points
step 1: find the slope
step 2: use the two point snd slope in Point-Slope
step 3: Solve for Y=mx + b
Number 1) (1,5) (2,7)
I have ten problems like this. Can you please work this problem out for me and I will be able to finish the last 9?
(Show me the work?)
Thank you.
cvanmol@aol.com
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Let's first identify your points:
P%5B1%5D:(x%5B1%5D,y%5B1%5D):(1,5)
P%5B2%5D:(x%5B2%5D,y%5B2%5D):(2,7)

That means that x%5B1%5D=1, y%5B1%5D=5, x%5B2%5D=2, and y%5B2%5D=7

Step 1: Find the slope:

The slope is given by m=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29

Just substitute the coordinate values:
m=%28%285-7%29%2F%281-2%29%29=%28-2%29%2F%28-1%29=2

Step 2:

Two point form: y-y%5B1%5D=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29%28x-x%5B1%5D%29

But notice that the big fraction on the right side of the two-point form is the same as the slope calculation, which allows us to write the point-slope form:

y-y%5B1%5D=m%28x-x%5B1%5D%29

Substituting, remembering that we said m=2 in step 1:

y-5=2%28x-1%29

Note that once you simplify the big fraction in the two-point form, the two-point and point-slope forms give you identical equations.

Step 3: Solve for y.

y-5=2%28x-1%29

Distribute:
y-5=2x-2

Add 5 to both sides:
y=2x%2B3

Check the answer: If we did this correctly, the x- and y-coordinates of the given points, when substituted into the equation for x and y, will make the equation a true statement.

5=2%281%29%2B3=2%2B3=5 True
7=2%282%29%2B3=4%2B3=7 True

Both true, answer checks.

Do the rest of your problems the same way. Hint: Be extremely cautious with signed numbers. Another hint: Check your work for every problem. If an answer doesn't check, the odds are good that you made a sign error. Good luck.

Super-Double-Plus-Extra Credit. What would have happened if I had identified the points the opposite way in the beginning of this problem, that is, if I had said (1,5) is P%5B2%5D and (2,7) is P%5B1%5D? Would I have gotten the same or different results at the end?