Question

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the standard form of the equation for this line?

Answer 1

That point slope equation given does not pass through those points, the point slope equation y + 7 = -0.4(x - 10) does, though. The standard form of that would be 

2x + 5y = -15

You can get that by distributing the -0.4 out

y + 7 = -0.4x + 4

You can then add 0.4x to both sides, and subtract 7 from both sides to get

0.4x + y = -3

Now some teachers may accept this, but in correct standard form the coefficient of x is a whole number, so you have to multiply both sides by 5 to get rid of the decimal, and you get