Question

Find an equation for the line that passes through the points , −6−5 and , 41 .

Answer 1

Answer:

3x-5y=7

Step-by-step explanation:

One way to write the equation of a line through two points is ...

... ∆y(x -x1) -∆x(y -y1) = 0

Here, ∆y = 1 -(-5) = 6, and ∆x = 4 -(-6) = 10. These two numbers have a common factor of 2 that can be removed, so we can use the values ...

... ∆y = 3, ∆x = 5 and fill in our equation as ...

... 3(x +6) -5(y +5) = 0 . . . using (-6, -5) for (x1, y1)

... 3x -5y -7 = 0 . . . . . . . . simplify; general form equation

... 3x -5y = 7 . . . . . . . . . . standard form equation

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Comment on 2-point form

Perhaps you more usually see the 2-point form of the equation of a line written as ...

... y -y1 = (y2 -y1)/(x2 -x1)·(x -x1)

If you call y2-y1 = ∆y and x2-x1 = ∆x, then you can multiply by ∆x to get

... ∆x(y -y1) = ∆y(x -x1) . . . . . this might be an easy form to remember

Subtracting the left side gives the form we used above:

... ∆y(x -x1) -∆x(y -y1) = 0