SOLUTION: So, we're supposed to find the slope and y-intercept for the following problem: (3,4) (5,7) and I know how ti work out the problem, I just can't set it up! I true m= 4-7 over 3-5

Algebra ->  Linear-equations -> SOLUTION: So, we're supposed to find the slope and y-intercept for the following problem: (3,4) (5,7) and I know how ti work out the problem, I just can't set it up! I true m= 4-7 over 3-5       Log On


   

Question 615924: So, we're supposed to find the slope and y-intercept for the following problem:
(3,4) (5,7) and I know how ti work out the problem, I just can't set it up! I true m= 4-7 over 3-5 but then I got stuck and knew it wasn't right. What do I do?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=3 and y%5B1%5D=4.
Also, is the second point . So this means that x%5B2%5D=5 and y%5B2%5D=7.


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


m=%287-4%29%2F%285-3%29 Plug in y%5B2%5D=7, y%5B1%5D=4, x%5B2%5D=5, and x%5B1%5D=3


m=%283%29%2F%285-3%29 Subtract 4 from 7 to get 3


m=%283%29%2F%282%29 Subtract 3 from 5 to get 2


So the slope of the line that goes through the points and is m=3%2F2


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-4=%283%2F2%29%28x-3%29 Plug in m=3%2F2, x%5B1%5D=3, and y%5B1%5D=4


y-4=%283%2F2%29x%2B%283%2F2%29%28-3%29 Distribute


y-4=%283%2F2%29x-9%2F2 Multiply


y=%283%2F2%29x-9%2F2%2B4 Add 4 to both sides.


y=%283%2F2%29x-1%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%283%2F2%29x-1%2F2


So the slope is 3%2F2 and the y-intercept is

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(3,4),(5,7)
slope = +%28+7+-+4+%29+%2F+%28+5+-+3+%29+=+3%2F2+
So far I have:
+y+=+%283%2F2%29%2Ax+%2B+b+
Now I can plug one of the given points back into equation
+4+=+%283%2F2%29%2A3+%2B+b+
+4+=+9%2F2+%2B+b+
+b+=+8%2F2+-+9%2F2+
+b+=+-1%2F2+
The equation is
+y+=+%283%2F2%29%2Ax+-1%2F2+
check:
Does it go through (5,7)?
+y+=+%283%2F2%29%2Ax+-1%2F2+
+7+=+%283%2F2%29%2A5+-1%2F2+
+7+=+15%2F2+-+1%2F2+
+7+=+14%2F2+
+14+=+14+
OK