SOLUTION: If possible please explain how you come up with each step.Thanks Find the equation, in slope-intercept form, of the line that passes through the points (5, 6) and (-7, 3).Than

Algebra ->  Graphs -> SOLUTION: If possible please explain how you come up with each step.Thanks Find the equation, in slope-intercept form, of the line that passes through the points (5, 6) and (-7, 3).Than      Log On


   



Question 107812: If possible please explain how you come up with each step.Thanks
Find the equation, in slope-intercept form, of the line that passes through the points (5, 6) and (-7, 3).Thanks

Found 3 solutions by checkley71, MathLover1, josmiceli:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
SLOPE=(Y2-Y1)/(X2-X1)
SLOPE=(3-6)/(-7-5)
SLOPE=-3/-12
SLOPE=1/4 ANSWER.
NOW SUBSTITUTE ONE SET OF (X,Y) VALUES IN THE LINE EQUATUION Y=mX+b & SOLVE FOR THE Y INTERCEPT (b).
6=1/4*5+b
6=5/4+b
b=6-5/4
b=(24-5)/4
b=19/4 THIS IS THE Y INTERCEPT.
THE EQUATION IS:
Y=X/4+19/4
+graph%28+300%2C+200%2C+-20%2C+5%2C+-10%2C+10%2C+y+=+x%2F4+%2B19%2F4%29+ (graph 300x200 pixels, x from -20 to 5, y from -10 to 10, y = x/4 +19/4).

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (5, 6) and (x2, y2) = (-7, 3).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%283-6%29%2F%28-7-5%29+=+0.25.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 0.25%2A5+%2Bb+=+4.75. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=6-0.25%2A5+=+4.75.

y=(0.25)x + (4.75)

Your graph:




Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The slope intercept form is y+=+mx+%2B+b
m is the slope, b is the y-intercept
Each point is a solution to the equation
(5,6)
6+=+m%2A5+%2B+b
(-7,3)
3+=+m%2A%28-7%29+%2B+b
now solve for m and b
multiply the 2nd equation by -1 and add to the 1st
3+=+m%2A%28-7%29+%2B+b
-3+=+m%2A7+-+b
add to
6+=+m%2A5+%2B+b
3+=+m%2A12
m+=+1%2F4
Now find b, by substitution in either equation-I'll use 1st
6+=+%281%2F4%29%2A5+%2B+b
multiply both sides by 4
24+=+5+%2B+4b
4b+=+19
b+=+19%2F4
So, the equation is y+=+%281%2F4%29%2Ax+%2B+19%2F4
Check answer by seeing if it goes through both points
6+=+%281%2F4%29%2A5+%2B+19%2F4
6+=+5%2F4+%2B+19%2F4
24%2F4+=+24%2F4 OK
also
3+=+%281%2F4%29%2A%28-7%29+%2B+19%2F4
3+=+-%287%2F4%29+%2B+19%2F4
12%2F4+=+12%2F4 OK