SOLUTION: Indicate in standard form the equation of the line passing through the given points. G(4, 6), H(1, 5)

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Question 885242: Indicate in standard form the equation of the line passing through the given points.
G(4, 6), H(1, 5)
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
To find the standard form of a line you need a point and then the slope of the line. We have two points given so we're set there so now we just need to find the slope between those points. The equation for slope is m=%28y2-y1%29%2F%28x2-x1%29. Now we can just plug in and find the slope:

m=%28y2-y1%29%2F%28x2-x1%29
m=%285-6%29%2F%281-4%29
m=-1%2F-3
where x1 and y1 are a point on
the line(in your case (4,6) and m is the slope of the line. Now we can just plug and chug:

y-y1=m%28x-x1%29Plug in your point and the slope
y-6=%281%2F3%29%2A%28x-4%29Distribute the 1/3
y-6=%281%2F3%29%2Ax-4%2F3Add 6 to both sides
y=%281%2F3%29%2Ax-4%2F3+%2B+6Get a common denominator
y=%281%2F3%29%2Ax-4%2F3+%2B+18%2F3Combine like terms
y=%281%2F3%29%2Ax%2B14%2F3+

Now we can put our answer in standard form. To do so we need to write it in the form of Ax+By=C. Which means we need to get x on the other side of the equation and clear the fractions.
y=%281%2F3%29%2Ax%2B14%2F3+Multiply both sides of the equation by 3 to clear the fractions.
3y=x%2B14+ subtract x from both sides.
-x%2B3y=14

2)Solving y=mx+b for b
The other way this can be solved is plugging in the point and the slope into y=mx%2Bb and solving for b. Remember the slope is 1/3 and the point we are using is (4,6).

y=mx%2BbPlug in the slope and the point into the formula
6=1%2F3%284%29%2BbMultiply
6=4%2F3%2Bb Subtract 4/3 from both sides
14%2F3+=+b

Now we now that b = 14/3 so we can plug that into our y=mx+b formula and get y=1/3x+14/3. Putting that in standard form as we did above you will see that you get the same answer.