The new line is parallel to the given line and therefore will have the same gradiient
Hence the gradient of the new line is 4/7 too
using
[tex]\begin{gathered} y-y_1=\text{ m}(x-x_{1)} \\ \text{where m is the gradient} \end{gathered}[/tex]In this case m = 4/7 and (x1,y1) = (-8,-6)
so substituting for x1 and y1 in the above equation
[tex]\begin{gathered} y\text{ - (-6) = 4/7(x -(-8))} \\ \end{gathered}[/tex]y +6 =4/7 (x +8)
y + 6 = 4/7x + (4/7 x8)
y + 6 = 4/7x + 32/7
y= 4/7x +32/7 -6
[tex]y\text{ = }\frac{4}{7}x\text{ -1}\frac{3}{7}[/tex]simplifying further
[tex]7y\text{ =4x -10}[/tex]