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x - y = - 6

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (3, 9)

m = = = 1, hence

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 9), then

9 = 3 + c ⇒ c = 9 - 3 = 6

y = x + 6 ← equation in slope- intercept form

Subtract y from both sides

0 = x - y + 6 ( subtract 6 from both sides )

- 6 = x - y, thus

x - y = - 6 ← in standard form