Question

The equation of line a is y= -8/5x + 4/3 line b is perpendicular to a what is th slope of line b​

Answer 1

The slope of line b is
`(5)/(8)`

Explanation:

• The product of the slopes of the perpendicular lines is -1

• That means if the slope of one of them is m, then the slope of the other is
  `-(1)/(m)`

• To find the slope of a perpendicular line to another line reciprocal its value and opposite its sign

• The form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

∵ The equation of line a is y =
`-(8)/(5)` x +
`(4)/(3)`

→ Compare it with the form of the equation above to find m

∴ m =
`-(8)/(5)`

∴ The slope of the line a is
`-(8)/(5)`

∵ Line b is perpendicular to line h

∴ The product of their slopes = -1

→ To find the slope of b reciprocal the slope of line a and change its sign

∵ The reciprocal of and opposite sign of
`-(8)/(5)` is
`(5)/(8)`

∴ The slope of line b is
`(5)/(8)`

To check your answer multiply the slopes they must give you -1

∵
`-(8)/(5)` ×
`(5)/(8)` = -1

∴ The answer is correct