Answer:
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Answer:
The answer to your question is 5x - 2y = 0
Step-by-step explanation:
Data
A (2, 5)
B (4, 10)
Process
1.- Determina the slope of the line
slope = m = (y2 - y1) / (x2 - x1)
x1 = 2 y1 = 5 x2 = 4 y2 = 10
-Substitution
m = (10 - 5) / (4 - 2)
-Simplification
m = 5/2
2.- Find the equation of the line in the general form
y - y1 = m(x - x1)
-Substitution
y - 5 = 5/2(x - 2)
-Simplification
2(y - 5) = 5(x - 2)
2y - 10 = 5x - 10
5x - 2y - 10 + 10 = 0
-Result
5x - 2y = 0
Infinite number of solutions...means it will be the same line.
you have probably heard about equivalent fractions like 1/2 = 2/4...and if u reduce 2/4, it equals 1/2. Well...there are also equivalent equations. They can also be reduced.
3y = 2x - 9 cant be reduced, but u can make an equivalent equation by multiplying it all by a number.Any number.
lets try 2...
2(3y = 2x - 9) =
6y = 4x - 18...this is an equivalent equation....the same line..infinite solutions.Notice that u can reduce it by dividing everything by 2 which would equal 3y = 2x - 9....so u see, it is like equivalent fractions....kind of...lol
or multiply it by 3
3(3y = 2x - 9) =
9y = 6x - 27....this is also equivalent.....so this is an answer as well
and u can multiply it by 4 and get another equivalent equation..or 5, or 6....and so on...
make any sense ?? Just remember, to get the result of infinite solutions, the equations have to be equivalent
