Question

Consider the line 3x+8y=1what is the slope of a line parallel to this line?what is the slope of a line perpendicular to this line?

Answer 1

To find the slope of the line given, we write the equation in slope-intercept form:

`y=mx+b`

For the equation,

`3x+8y=1`

subtracting 3x from both sides gives

`8y=1-3x`

Finally, dividing both sides by 8 gives

`y=(1-3x)/(8)`

which can be rearranged and written as

`y=-(3)/(8)x+(1)/(8)`

Hence, the slope of the line parallel to the given line is -3/8.

To find the slope of the perpendicular line, we have to remember that

`m_(\perp)=-(1)/(m)`

Since m = -3/8, the above gives

`m_(\perp)=-(1)/((-(3)/(8)))`

Simplifying the above gives

`m_(\perp)=(8)/(3)`

Hence, the slope of the perpendicular line is 8/3.