Two lines are parallel if they have the same slope. In order to better visualize the slope of the line we will express it in the slope-intercept form, which is done below:
[tex]\begin{gathered} \frac{1}{5}x-\frac{1}{6}y\text{ = 7} \\ \frac{1}{5}x-7=\frac{1}{6}y \\ \frac{1}{6}y\text{ = }\frac{1}{5}x-7 \\ y\text{ = }\frac{6}{5}x\text{ - 42} \end{gathered}[/tex]We now know that the slope of the line is 6/5, because in this form the slope is always the number that is multiplying the "x" variable. So we need to find a line of the type:
[tex]h(x)\text{ = }\frac{6}{5}x+b[/tex]Therefore the only needed variable is "b", which we can find by applying the known point (-5, -10).
[tex]\begin{gathered} -10\text{ = }\frac{6}{5}\cdot(-5)\text{ + b} \\ -10=-6+b \\ b=-10+6 \\ b=-4 \end{gathered}[/tex]The expression of the line is then:
[tex]h(x)\text{ = }\frac{6}{5}x-4[/tex]