Explanation:
the equation
y = -8/5 x + 6
tells us 2 things :
-8/5 is the slope of the line, 6 is the y-intercept (the y value when x = 0).
a parallel line has the same slope (just a different y-intercept) : -8/5
a perpendicular line (intercepts at 90°) turns the original slope upside-down and flips the sign : 5/8
we the use the given point as x and y values and calculate the y-intercepts.
parallel :
3 = -8/5 × 5 + y-intercept = -8 + y-intercept
11 = y-intercept
y = -8/5 x + 11
perpendicular :
3 = 5/8 × 5 + y-intercept = 25/8 + y-intercept
(3×8)/8 = 24/8 = 25/8 + y-intercept
-1/8 = y-interceot
y = 5/8 x - 1/8 = 1/8 × (5x - 1)