Question

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,6) and perpendicular to 3 x + 7y = 1.a) The equation of the line in slope-intercept form is   enter your response here

Answer 1

The equation

`3x+7y=1`
`7y=-3x+1`
`y=(-3x)/(7)+(1)/(7)`

has slope -3/7.

The product of perpendicular lines must be -1, so the slope of the new equation must be:

`m\cdot-(3)/(7)=-1`
`m=(-1\cdot7)/(-3)=(7)/(3)`

The line with that slope and that passes throught (1,6) is:

`(y-6)=m(x-1)`
`(y-6)=(7)/(3)(x-1)`
`y-6=(7)/(3)x-(7)/(3)`
`y=(7)/(3)x-(7)/(3)+6`
`y=(7)/(3)x-(7)/(3)+(18)/(3)`
`y=(7)/(3)x+(11)/(3)`

The following graph shows both equations:

`y=(7)/(3)x+(11)/(3)`
`3\cdot y=((7)/(3)x+(11)/(3))\cdot3`
`3y=7x+11`
`-7x+3y=11`