Question

Determine the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3

Answer 1

SOLUTIONS

The parallel line will be of form

`m_1=m_2`

the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3

`\begin{gathered} -4y-3x=-3 \\ -4y=3x-3 \\ y=(3x)/(-4)-(3)/(-4) \\ y=-(3)/(4)x+(3)/(4) \\ y=mx+c \\ m_1=-(3)/(4) \end{gathered}`

The equation of the line parallel to point(1/7 , 1)

`\begin{gathered} y-y_1=m(x-x_1) \\ x_1=(1)/(7),y_1=1 \\ y-1=-(3)/(4)(x-(1)/(7)) \\ y-1=-(3)/(4)x+(3)/(28) \\ y=-(3)/(4)x+(3)/(28)+1 \\ multiply\text{ through by 28} \\ 28y=-21x+3+28 \\ 28y=-21x+31 \end{gathered}`