Question

The lines given by the equations 3y + 2x = 7 and y = mx − 11 are perpendicular. Find m

Answer 1

`m=(3)/(2)`

Explanation:

When two lines are perpendicular, their slopes will be opposite reciprocals:

`-3` →
`(1)/(3)`

`(1)/(4)` →
`-4`

Solve the first equation for y to rewrite in slope-intercept form:

`y=mx+b\\\\3y+2x=7\\\\3y+2x-2x=7-2x\\\\3y=-2x+7\\\\(3y)/(3)=(-2x)/(3) +(7)/(3) \\\\y=-(2)/(3)x+(7)/(3)`

m is the slope, so the slope of this line is
`-(2)/(3)`. The opposite reciprocal is
`(3)/(2)`, therefore, m is
`(3)/(2)`