Consider the line 2x-7y=-7. Find the equation of the line that is perpendicular to this line and passes through the point (-8,-6). Find the equation of the line that is parallel to this line and passes through the point(-8,-6).

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