To identify the slope and y-intercept, we will take the given equation to its slope-intercept form:
[tex]y=mx+b,[/tex]where m is the slope and b is the y-intercept.
To take the equation to its slope-intercept form, we add 3y to the given equation:
[tex]\begin{gathered} 5x-3y+3y=9+3y, \\ 5x=9+3y\text{.} \end{gathered}[/tex]Now, we subtract 9, and get:
[tex]5x-9=3y\text{.}[/tex]Finally, dividing by 3, we get:
[tex]y=\frac{5}{3}x-3.[/tex]Therefore, the slope and y-intercept are:
[tex]\frac{5}{3},\text{ and -3 }[/tex]correspondingly.
Answer:
Slope:
[tex]\frac{5}{3}\text{.}[/tex]Y-intercept:
[tex]-3.[/tex]