slope int form:
[tex]y = mx + b[/tex]
since the other line is parallel it will have the same slope as the line you are trying to figure out and it is already in slope intercept form. The slope of the parallel line is 9/4 so our slope will also be 9/4. We can put this in our equation.
[tex]y = \frac{9}{4} x + b[/tex]
Now we need to find b. To do this plug in the coordinate points given to you (3,4)
[tex]4 = ( \frac{9}{4} )(3) + b[/tex]
solve for b
[tex]b = 4 - \frac{9 \times 3}{4} = ( \frac{16}{4} - \frac{27}{4} ) = - \frac{ 11}{4} [/tex]
so the slope int form would be
[tex]y = ( \frac{9}{4} )x - \frac{11}{4} [/tex]
