Step-by-step explanation:
2x - 7y = -7
2x + 7 = 7y
y = (2/7)x + 1
the slope of the line is the factor of x : 2/7
FYI that is the ratio y/x and means, when x changes by 7 points to the plus (right) side, then y changes 2 points to the plus (up) side.
the parallel line will have the same slope, of course. just a different y-axis-interception point. that means, the "+" term at the end changes. changes to what ?
well, we use the given point coordinates
-6 = (2/7)×-8 + c
-6 = -16/7 + c
-42/7 = -16/7 + c
-26/7 = c
so, the equation of the parallel line is
y = (2/7)x - 26/7
y = (2/7)×(x - 13)
the perpendicular line is a line that intercepts our original line with a 90 degree angle.
that means its slope will switch x and y of the original line slope and also flips the sign (from + to - or vice versa).
=> the slope of the perpendicular line is -7/2.
the line equation looks like
y = (-7/2)x + c
and again, we use the given point coordinates to find the missing c (y-intercept).
-6 = (-7/2)×-8 + c
-6 = -7×-4 +c
-6 = 28 + c
-34 = c
so, the full equation of the perpendicular line is
y = (-7/2)x - 34
