Question

Which equation is the slope-intercept form of the line that passes through (6, –11) and is parallel to the graph of y = –2/3x + 12?A.y = –2/3x – 7B.y = –2/3x – 6C.y = 2/3x – 5D.y = 2/3x – 15

Answer 1

For Parallelism condition; the slope are equal, i.e;

`M_1=M_2`

From the given straight line equation:

`\begin{gathered} y=-(2)/(3)x+12 \\ M_1=-(2)/(3) \end{gathered}`
`\begin{gathered} \text{For Parallel lines:} \\ M_1=M_2 \\ \text{Thus, M}_2=-(2)/(3) \end{gathered}`

From the given point (6, - 11);

`x_1=6;y_1=-11`

Since we have the given points and know the value of the slope, thus we have:

`\begin{gathered} M_2=(y-y_1)/(x-x_1) \\ -(2)/(3)=(y-(-11))/(x-6) \\ -(2)/(3)=(y+11)/(x-6) \\ \text{cross}-\text{multiply} \\ 3(y+11)=-2(x-6) \\ 3y+33=-2x+12 \\ 3y=-2x+12-33 \\ 3y=-2x-21 \\ (3y)/(3)=-(2x)/(3)-(21)/(3) \\ y=-(2)/(3)x-7 \end{gathered}`

Hence, the correct option is A