Two equations are paralell if they have the same slope.
Then to find the paralell equation to [tex]5x-4y=8[/tex], we can do the following: clear out y as a function of x, to get the intercept and the slope that accompanies x.
To do this, we follow the next steps: 1) subtract 5x both sides of the equation (which results in [tex]-4y=8-5x[/tex]; 2) divide both sides by (-4), would yield [tex]y=1.25x-2[/tex].
Now we have an clear expression of y as a function of x, and can find a parallel line that passes through (x,y)=(4,9). This new equation shall be an expression that meets the following: 9=1.25 (4)+h, where we do not know the value of h, and the values of (x,y) have been replaced by the point required.
If we solve the equation above, we obtain the value of h (intercept) for our parallel equation: h=4.
Then, the parallel equation that passes through (4,9) is y=1.25x+4 (to verify this is ok, replace x=4 in this equation, and you will get y=9, which is what we were lloking for: a parallel equation to y=1.25x-2 that passes through (4,9)
