Question

Find an equation for the line that passes through the points , −4−5 and , 2,5 .

Answer 1

Answer:

5x -3y = -5

Step-by-step explanation:

One formula that is useful for writing equations of lines through two points is ...

... (x2 -x1)(y -y1) = (y2 -y1)(x -x1)

Using the given points, this becomes ...

... (2 -(-4))(y -(-5)) = (5 -(-5))(x -(-4))

... 6(y +5) = 10(x +4) . . . . simpify

We can divide by 2 and subtract the left side to get ...

... 0 = 5x +20 -3y -15

... 0 = 5x -3y +5 . . . . . . . this is the general form equation of a line

Subtracting the constant gives the standard form equation.

... 5x -3y = -5

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Comment on the solution

As a rule, writing the equation this way from integer coefficients avoids fractions entirely. In the form with x on one side and y on the other, you can choose to move the x-term or leave it be, in order to ensure that it has a positive coefficient in the final equation. (Here we left it alone and moved the y-term.)

The standard form requires that the numbers in the equation be relatively prime (no common factors). That is why we divided by the common factor 2 in the development above.