Given
The equations are,
[tex]\begin{gathered} 2x+y=7\text{ \_\_\_\_\_\_\_\_\lparen1\rparen} \\ y-5=2x\text{ \_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]To find the slope intercept form and to check whether the lines are parallel or perpendicular.
Explanation:
It is given that,
[tex]\begin{gathered} 2x+y=7\text{ \_\_\_\_\_\_\_\_\lparen1\rparen} \\ y-5=2x\text{ \_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]Since the slope intercept form is defined as,
[tex]\begin{gathered} y=mx+c \\ where,\text{ }m\text{ }is\text{ }the\text{ }slope. \end{gathered}[/tex]Then, (1) can be written as,
[tex]\begin{gathered} y=-2x+7 \\ Here,\text{ }m_1=-2.\text{ \_\_\_\_\lparen3\rparen} \end{gathered}[/tex]And, (2) can be written as,
[tex]\begin{gathered} y=2x+5 \\ Here,\text{ }m_2=2.\text{ \_\_\_\_\lparen4\rparen} \end{gathered}[/tex]From (3) and (4),
[tex]\begin{gathered} m_1\ne m_2 \\ m_1\times m_2\ne-1 \end{gathered}[/tex]Hence, the equations are neither parallel nor perpendicular.
