We know that parallel lines have the same slope, this means that the searched line has the form
[tex]y=\frac{7}{5}x+b[/tex]This is because the slope is the coefficient of x on the given line equation:
[tex]y=\frac{7}{5}x+4[/tex]Now, we can find by y-intercept, denoted by b, by substituting the given point (5,2) into our line from above, that is,
[tex]2=\frac{7}{5}(5)+b[/tex]which gives
[tex]2=7+b[/tex]then, by subtracting 7 to both sides, we get
[tex]-5=b[/tex]or equivalently,
[tex]b=-5[/tex]Finally, by substituting this value into our line model, the answer is:
[tex]y=\frac{7}{5}x-5[/tex]