Respuesta :
We are given the following two equations.
[tex]y-7x=3\qquad and\qquad 14x-2y=28[/tex]We are asked to find out whether these equations of lines are parallel, perpendicular, or neither.
First of all, let us re-write these equations into the standard slope-intercept form.
This simply means to separate the y variable.
[tex]\begin{gathered} y-7x=3 \\ y=7x+3\qquad eq.1 \end{gathered}[/tex]Similarly, for the other equation
[tex]\begin{gathered} 14x-2y=28 \\ 14x=2y+28 \\ 14x-28=2y \\ 2y=14x-28 \\ y=\frac{14x}{2}-\frac{28}{2} \\ y=7x-14\qquad eq.2 \end{gathered}[/tex]Now recall that the standard slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Comparing the standard form with our two equations we see that
Slope of 1st equation = 7
Slope of 2nd equation = 7
So the two equations have an equal slope.
Whenever two equations have equal slopes then the lines are parallel.
Therefore, the given equations are parallel.
