Respuesta :
[tex]\text{The equation for line I is 4x - y = -2 ( Option A)}[/tex]
The equation for the second line is:
[tex]4x\text{ - y = 1}[/tex][tex]\text{The general equation of a line is y = mx + c}[/tex]Where m = slope and c = Intercept
Let us rewrite the given equation in that form :
[tex]\text{ y = 4x - 1}[/tex]Comparing y = 4x - 1 with y = mx + c:
m = 4 and c = -1
Since line I is parallel to the given line, it means their slopes are equal. Therefore, the slope for line I is also m = 4
Line I contains the Point:
[tex](x_1,y_{1)\text{ = }}(0,\text{ 2)}[/tex]The equation of a line can also be written in the form:
[tex]y-y_1=m(x-x_{1\text{ }})[/tex][tex]y\text{ - 2 = 4 (x - 0)}[/tex][tex]y\text{ - 2 = 4x}[/tex]By rearranging the above equation:
[tex]4x\text{ - y = -2}[/tex]The above is the equation for line I
