Lets write the equation in slope-intercept form
[tex]y=mx+b,[/tex]where m is the slope and b is the y-intercept.
Then, we have
[tex]\begin{gathered} 3y=-5-2x \\ y=-\frac{2}{3}x-\frac{5}{3} \end{gathered}[/tex]By comparing equations, we can note that the y-intercept is
[tex]\begin{gathered} \\ b=-\frac{5}{3} \end{gathered}[/tex]Now, the x-intercept occurs at y=0. By substituting this value into our line equation, we get
[tex]0=-\frac{2}{3}x-\frac{5}{3}[/tex]then, the x-intercept is given by
[tex]\begin{gathered} -\frac{2}{3}x=\frac{5}{3} \\ x=-\frac{\frac{5}{3}}{\frac{2}{3}} \\ x=-\frac{5\cdot3}{2\cdot3} \\ x=-\frac{5}{2} \end{gathered}[/tex]Therefore, the answer is
- x intercept is -5/2
- y-intercept is -5/3
