Question

which of the following linear equations is a line that passes through the point (-3,3) and is parallel to the given line?

Answer 1

`\begin{gathered} you\text{ must choose 2 points of the given line, for example} \\ (x_1,y_1)=(0,-3)and(x_2,y_2)=(-3,-1) \\ \text{and compute the slope} \\ m=(y_2-y_1)/(x_2-x_1) \end{gathered}`
`\begin{gathered} by\text{ substituying those points in m, one has} \\ m=(-1-(-3))/(-3-0) \\ m=(-1+3)/(-3) \\ m=(2)/(-3) \\ m=-(2)/(3) \end{gathered}`
`\begin{gathered} \sin ce\text{ the unknow line must be parallel, it must have the same slope. Hence, } \\ y=-(2)/(3)x+b \\ \text{and b can be solved with the information that, the lines passes throgh (-3,3), then} \\ 3=-(2)/(3)(-3)+b \\ 3=(2\cdot3)/(3)+b \\ 3=2+b \\ 3-2=b \\ 1=b\Rightarrow b=1 \\ \text{The solution is} \\ y=-(2)/(3)x+1 \end{gathered}`