Question

Determine whether the lines are parallel, intersect, or coincidingY = 5x - 2X + 4y = 8

Answer 1

Given:

The equation of line is,

`\begin{gathered} y=5x-2\Rightarrow5x-y-2=0\ldots\ldots\ldots\ldots........(1) \\ x+4y=8\Rightarrow x+4y-8=0\ldots.\ldots..\ldots...(2) \end{gathered}`

For the equation,

`\begin{gathered} A_1x+B_1y+C_1=0 \\ A_2x+B_2y+C_2=0 \end{gathered}`

`\begin{gathered} \text{Parallel line if : }(A_1)/(A_2)=(B_1)/(B_2) \\ \text{ Coinside line if : }(A_1)/(A_2)=(B_1)/(B_2)=(C_1)/(C_2) \\ \text{Intersect line if : }(A_1)/(A_2)\\e(B_1)/(B_2) \end{gathered}`

For the given equation of lines,

`\begin{gathered} (A_1)/(A_2)=(5)/(1) \\ (B_1)/(B_2)=-(1)/(4) \\ \Rightarrow(A_1)/(A_2)\\e(B_1)/(B_2) \end{gathered}`

Hence, the given lines are intersect each other.