In order to find the parallel line that passes through H, we need to know that parallel lines have the same slope.
So first, let's calculate the slope of line JY using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope between points (x1, y1) and (x2, y2).
So, for points J(3, -4) and Y(-2, 5), we have:
[tex]m=\frac{5-(-4)_{}}{-2-3}=\frac{9}{-5}=-\frac{9}{5}[/tex]
Now, let's use this slope and point H in the slope-intercept form of the linear equation:
[tex]\begin{gathered} y=mx+b \\ (0,3)\colon \\ 3=-\frac{9}{5}\cdot0+b \\ b=3 \end{gathered}[/tex]
Therefore the equation is y = (-9/5)x + 3
