Question

what is the slope of a line perpendicular to this linewhat is the slope of a line parallel to this line

Answer 1

• Slope perpendicular to the line: 8/5

,

• Slope parallel to the line: –5/8

Step-by-step explanation

Given

`5x+8y=7`

To know the result, it is better if we work with the slope-intercept form:

`y=mx+b`

Then, to get this kind of form we have to isolate y from the given equation:

`8y=7-5x`
`y=(7-5x)/(8)`
`y=-(5)/(8)x+(7)/(8)`

Thus, in this case, m = –5/8 and b = 7/8.

Perpendicular lines have negative reciprocal lines:

`m_2=-(1)/(m_1)`

where m₁ is the slope of line 1 and m₂ is the line perpendicular to line 1.

Then, replacing the values:

`m_2=-(1)/(-(5)/(8))`
`m_2=(8)/(5)`

Finally, the slopes of parallel lines are the same, meaning:

`m_2=m_1`

where m₁ is the slope of line 1 and m₂ is the line parallel to line 1.