Answer :
ANSWER
[tex]y=\frac{5}{6}x-\frac{5}{3}[/tex]EXPLANATION
We want to find the slope-intercept form of the equation:
[tex]5x-6y=10[/tex]The slope intercept form of a linear equation is given as:
[tex]y=mx+b[/tex]where m = slope; b = y intercept
Therefore, we have to make y subject of formula:
[tex]\begin{gathered} 5x-6y=10 \\ \text{Subtract 5x from both sides of the equation:} \\ 5x-6y-5x=10-5x \\ -6y=-5x+10 \\ \text{Divide both sides by -6:} \\ -\frac{6y}{-6}=\frac{-5x+10}{-6} \\ y=\frac{5}{6}x-\frac{10}{6} \\ y=\frac{5}{6}x-\frac{5}{3} \end{gathered}[/tex]That is the equation in slope-intercept form.