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\frac{y+5}{-7-\left(-5\right)}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
The opposite of -5 is 5.
\frac{y+5}{-7+5}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
The opposite of -5 is 5.
\frac{y+5}{-2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
Add -7 and 5 to get -2.
\frac{-y-5}{2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
Multiply both numerator and denominator by -1.
\frac{-y-5}{2}=\frac{x+2}{3-\left(-2\right)}
The opposite of -2 is 2.
\frac{-y-5}{2}=\frac{x+2}{3+2}
The opposite of -2 is 2.
\frac{-y-5}{2}=\frac{x+2}{5}
Add 3 and 2 to get 5.
-\frac{1}{2}y-\frac{5}{2}=\frac{x+2}{5}
Divide each term of -y-5 by 2 to get -\frac{1}{2}y-\frac{5}{2}.
-\frac{1}{2}y-\frac{5}{2}=\frac{1}{5}x+\frac{2}{5}
Divide each term of x+2 by 5 to get \frac{1}{5}x+\frac{2}{5}.
\frac{1}{5}x+\frac{2}{5}=-\frac{1}{2}y-\frac{5}{2}
Swap sides so that all variable terms are on the left hand side.
\frac{1}{5}x=-\frac{1}{2}y-\frac{5}{2}-\frac{2}{5}
Subtract \frac{2}{5} from both sides.
\frac{1}{5}x=-\frac{1}{2}y-\frac{29}{10}
Subtract \frac{2}{5} from -\frac{5}{2} to get -\frac{29}{10}.
\frac{1}{5}x=-\frac{y}{2}-\frac{29}{10}
The equation is in standard form.
\frac{\frac{1}{5}x}{\frac{1}{5}}=\frac{-\frac{y}{2}-\frac{29}{10}}{\frac{1}{5}}
Multiply both sides by 5.
x=\frac{-\frac{y}{2}-\frac{29}{10}}{\frac{1}{5}}
Dividing by \frac{1}{5} undoes the multiplication by \frac{1}{5}.
x=\frac{-5y-29}{2}
Divide -\frac{y}{2}-\frac{29}{10} by \frac{1}{5} by multiplying -\frac{y}{2}-\frac{29}{10} by the reciprocal of \frac{1}{5}.
\frac{y+5}{-7-\left(-5\right)}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
The opposite of -5 is 5.
\frac{y+5}{-7+5}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
The opposite of -5 is 5.
\frac{y+5}{-2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
Add -7 and 5 to get -2.
\frac{-y-5}{2}=\frac{x-\left(-2\right)}{3-\left(-2\right)}
Multiply both numerator and denominator by -1.
\frac{-y-5}{2}=\frac{x+2}{3-\left(-2\right)}
The opposite of -2 is 2.
\frac{-y-5}{2}=\frac{x+2}{3+2}
The opposite of -2 is 2.
\frac{-y-5}{2}=\frac{x+2}{5}
Add 3 and 2 to get 5.
-\frac{1}{2}y-\frac{5}{2}=\frac{x+2}{5}
Divide each term of -y-5 by 2 to get -\frac{1}{2}y-\frac{5}{2}.
-\frac{1}{2}y-\frac{5}{2}=\frac{1}{5}x+\frac{2}{5}
Divide each term of x+2 by 5 to get \frac{1}{5}x+\frac{2}{5}.
-\frac{1}{2}y=\frac{1}{5}x+\frac{2}{5}+\frac{5}{2}
Add \frac{5}{2} to both sides.
-\frac{1}{2}y=\frac{1}{5}x+\frac{29}{10}
Add \frac{2}{5} and \frac{5}{2} to get \frac{29}{10}.
-\frac{1}{2}y=\frac{x}{5}+\frac{29}{10}
The equation is in standard form.
\frac{-\frac{1}{2}y}{-\frac{1}{2}}=\frac{\frac{x}{5}+\frac{29}{10}}{-\frac{1}{2}}
Multiply both sides by -2.
y=\frac{\frac{x}{5}+\frac{29}{10}}{-\frac{1}{2}}
Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.
y=\frac{-2x-29}{5}
Divide \frac{x}{5}+\frac{29}{10} by -\frac{1}{2} by multiplying \frac{x}{5}+\frac{29}{10} by the reciprocal of -\frac{1}{2}.