Given:
Line a is parallel to line b.
1) Line a passes through the points (1,5) and (2,-4).
Its slope is estimated as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(1,5) \\ (x_2,y_2)=(2,-4) \\ m=\frac{-4-5}{2-1}=\frac{-9}{1}=-9 \end{gathered}[/tex]As the given 2 lines are parallel , it implies that their slope must be equal.
[tex]\text{therefore, the slope of line b=-9}[/tex]The equation of line b having slope -9 and passing through point (1,12) is given by,
[tex]\begin{gathered} y-y_1=m(x-x_1)\ldots(\text{ Slope intercept form)} \\ (x_1,y_1)=(1,12) \\ y-12=-9(x-1) \\ y-12=-9x+9 \\ y+9x-21=0 \end{gathered}[/tex]Answer: The equation of line b is y = -9x + 21.
