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.