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 <em>general form</em> equation of a line
Subtracting the constant gives the <em>standard form</em> equation.
... 5x -3y = -5
_____
<em>Comment on the solution</em>
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.
