Answer:
2x - 5y = 20
Explanation:
Standard form should look like:
Ax + By = C
and the numbers A,B, and C have to be whole numbers (actually integers, because negative is okay too except A has to be positive)
You have been given a point and the slope. There is a shortcut, fill-in-the-blank equation called point-slope that you can just fill in a point and the slope. Then we can change that equation into standard form.
Point-slope equation:
y - Y = m(x - X)
Fill in (5, -2), which is the (X, Y). 5 in place of X and -2 in place of Y. Fill in 2/5 for the m which is slope.
y - Y = m(x - X)
y - -2 = 2/5(x - 5)
simplify, and distribute.
y + 2 = 2/5x - 2
Multiply through by 5 to get rid of the fraction.
5y + 10 = 2x - 10
Subtract 10.
5y = 2x -20
Subtract 2x.
5y - 2x = -20
Rearrange the terms.
-2x + 5y = -20
Multiply through by -1 (because that A has to be positive)
2x - 5y = 20
The equation in standard form is:
2x - 5y = 20