Question

Plz help me! I really appreciate it

Answer 1

The equation y =
`-(8)/(7)` x - 7 represents a line perpendicular to the given line

Explanation:

The product of the slopes of the perpendicular lines is -1, which means if the slope of one line is m, then the slope of the perpendicular line to it is
`(-1)/(m)` (negative reciprocal)

• The slope of the equation ax + by = c is
  `(-a)/(b)`, where a, b, c are constant

• The slope of the equation y = m x + b is m

Let us solve the question

∵ The equation of the given line is 7x - 8y = 16

∴ a = 7 and b = -8

→ Use the rule above to find the slope of it

∵ The slope of the given line =
`(-7)/(-8)`

∴ The slope of the given line =
`(7)/(8)`

To find the slope of the perpendicular line to it reciprocal the fraction and change its sign

∴ The slope of the perpendicular line =
`-(8)/(7)`

→ Look at the answer to find the equation which has this slope

∴ The equation of the perpendicular line is y =
`-(8)/(7)` x - 7