The first thing we have to know is that parallel lines have the same slope. The slope can be identified in the general equation of the line:
[tex]\begin{gathered} y=mx+b \\ m\to\text{slope} \\ b\to y-\text{intercept} \end{gathered}[/tex]
Taking that into account, we identify the slope of the given line
[tex]\begin{gathered} y=-\frac{2}{3}x+\frac{3}{2} \\ m=-\frac{2}{3} \\ b=\frac{3}{2} \end{gathered}[/tex]
Now we replace the slope in the general equation
[tex]y=-\frac{2}{3}x+b[/tex]
With the given point we can find the intercept value of y and thus be able to have the equation of our parallel line
[tex]\begin{gathered} (4,-7)\to\text{given point} \\ -7=-\frac{2}{3}(4)+b \\ b=-7+\frac{8}{3} \\ b=-\frac{13}{3} \end{gathered}[/tex]
The equation of the parallel line that passes through the point (4, -7) is
[tex]y=-\frac{2}{3}x-\frac{13}{3}[/tex]
using the slash it would be: y = 2/3x-13/3
