The slope-intercept form of a line is given by:
[tex]\begin{gathered} y=mx+b \\ where\colon \\ m=slope \\ b=y-intercept_{} \end{gathered}[/tex]so:
[tex]-5x+3y=-7.5[/tex]solve for y:
[tex]\begin{gathered} 3y=5x-7.5 \\ y=\frac{5}{3}x-\frac{5}{2} \\ \end{gathered}[/tex]So:
[tex]\begin{gathered} m=\frac{5}{3} \\ b=-\frac{5}{2} \end{gathered}[/tex]The x-intercept is:
[tex]\begin{gathered} y=0 \\ 0=\frac{5}{3}x-\frac{5}{2} \\ \frac{5}{3}x=\frac{5}{2} \\ x=\frac{15}{10}=1.5 \end{gathered}[/tex]