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y+2=\frac{2}{3}\left(x-5\right)
The opposite of -2 is 2.
y+2=\frac{2}{3}x-\frac{10}{3}
Use the distributive property to multiply \frac{2}{3} by x-5.
\frac{2}{3}x-\frac{10}{3}=y+2
Swap sides so that all variable terms are on the left hand side.
\frac{2}{3}x=y+2+\frac{10}{3}
Add \frac{10}{3} to both sides.
\frac{2}{3}x=y+\frac{16}{3}
Add 2 and \frac{10}{3} to get \frac{16}{3}.
\frac{\frac{2}{3}x}{\frac{2}{3}}=\frac{y+\frac{16}{3}}{\frac{2}{3}}
Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.
x=\frac{y+\frac{16}{3}}{\frac{2}{3}}
Dividing by \frac{2}{3} undoes the multiplication by \frac{2}{3}.
x=\frac{3y}{2}+8
Divide y+\frac{16}{3} by \frac{2}{3} by multiplying y+\frac{16}{3} by the reciprocal of \frac{2}{3}.
y+2=\frac{2}{3}\left(x-5\right)
The opposite of -2 is 2.
y+2=\frac{2}{3}x-\frac{10}{3}
Use the distributive property to multiply \frac{2}{3} by x-5.
y=\frac{2}{3}x-\frac{10}{3}-2
Subtract 2 from both sides.
y=\frac{2}{3}x-\frac{16}{3}
Subtract 2 from -\frac{10}{3} to get -\frac{16}{3}.