y = 2x - 5
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 2x - y = 6 into this form ( subtract 2x from both sides )
- y = - 2x + 6 ( multiply through by - 1 )
y = 2x - 6 ← in slope -intercept form with slope m = 2
Parallel lines have equal slopes
the partial equation is y = 2x + c
to find c substitute (2, - 1 ) into the partial equation
- 1 = 4 + c ⇒ c = - 1 - 4 = - 5
y = 2x - 5 ← equation of parallel line