Question

Find the equation of line b described below in slope intercept formLine a is parallel to line bLine a passes through the points (1,5) and (2,-4)Line b passes through the point (1,12)

Answer 1

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,

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ (x_1,y_1)=(1,5) \\ (x_2,y_2)=(2,-4) \\ m=(-4-5)/(2-1)=(-9)/(1)=-9 \end{gathered}`

As the given 2 lines are parallel , it implies that their slope must be equal.

`\text{therefore, the slope of line b=-9}`

The equation of line b having slope -9 and passing through point (1,12) is given by,

`\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}`

Answer: The equation of line b is y = -9x + 21.