The given equation is
[tex]x-2y=-7[/tex]First, we find the slope of the given equation.
[tex]\begin{gathered} -2y=-7-x \\ y=\frac{-7-x}{-2} \\ y=\frac{7}{2}+\frac{x}{2} \end{gathered}[/tex]Remember that the slope is the coefficient of x. So, the slope of the given line is 1/2.
Since the new line must be parallel, then its slope is also 1/2.
According to the problem, the new line passes through (-3, -3). Let's use the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=\frac{1}{2}(x-(-3)) \\ y+3=\frac{1}{2}x+\frac{3}{2} \\ y=\frac{1}{2}x+\frac{3}{2}-3 \\ y=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]
