2x - y = 2
obtain the equation of the line in slope-intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (- 1, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{-1-2}[/tex] = [tex]\frac{-6}{-3}[/tex] = 2
the line crosses the y-axis at (0, - 2 ) ⇒ c = - 2
y = 2x - 2 ← in point-slope form
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
rearrange y = 2x - 2 into this form
subtract y from both sides
0 = 2x - y - 2 ( add 2 to both sides )
2x - y = 2 ← in standard form
