Respuesta :

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]