a)y=4x-28
Explanation
the equation of a line can be written as follows
[tex]\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ and\text{ b is the y-intercept} \end{gathered}[/tex]Step 1
a) find the slope of the given line
[tex]\begin{gathered} y=4x+2\Rightarrow y=mx+b \\ hence \\ slope_1=4 \end{gathered}[/tex]b)now, 2 lines are parallel it the slope is the same in both lines, so
the slope of the line we are looking for must be 4 as well
[tex]\begin{gathered} slope_1=slope_2 \\ 4=slope_2 \end{gathered}[/tex]so
Slope = 4
Step 2
finally, use the slope -point formula to find the equation of the line
[tex]\begin{gathered} slope-point\text{ formula} \\ y-y_1=m(x-x_1) \\ where\text{ m is the slope} \\ \text{ \lparen x}_1,y_1)\text{ is a point of the lines} \end{gathered}[/tex]a) let
[tex]\begin{gathered} point\text{ =\lparen8,4\rparen} \\ slope=\text{ 4} \end{gathered}[/tex]b) now, replace and isolate y
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-(4)=4(x-8) \\ y-4=4x-32 \\ add\text{ 4 in both sides} \\ y-4+4=4x-32+4 \\ y=4x-28 \end{gathered}[/tex]therefore, the answer is
a)y=4x-28
I hope this helps you
