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How do you find the distance between the 2 parallel lines if the problem gives you y=-x and y=-x-4

Mathematics
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Solve them simultaneously
Line 1) y = 2/7x + 4 Line 2) y = 2/7x - 2 Pick a point on line 1 - (7/2 ,5) Now find the equation of the line that is perpendicular to line 1 and passes through (7/2, 5) y - 5 = (-7/2)(x - 7/2) y - 5 = (-7/2)x + 49/4 y = (-7/2)x +69/4 Now find the point where this perpendicular line crosses line 2: (2/7)x - 2 = (-7/2)x + 69/4 (4/14)x - 8/4 = (-49/14)x + 69/4 (53/14)x = 77/4 x = 1078/212 = 539/106 Plug this value for x into line 2 to find the y coordinate y = (2/7)(539/106) - 2 y = 1078/742 - 1484/742 y = -406/742 = -29/53 The the perpendicular line crosses line 1 at (7/2, 5) and line 2 at (539/106, -29/53) so to find the distance between these points lets use the distance formula: d = SQRT((-29/53 - 5)^2 + (539/106 - 7/2)^2) d = 5.77 rounded to the nearest hundreths

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