Solve y=frac{a_{m}-a_{n}}{m-n}

$$y = \frac { a _ { m } - a _ { n } } { m - n }$$

Solve for a_n

$$a_{n}=ny-my+a_{m}$$

$$m\neq n$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m-n.

$$y\left(m-n\right)=a_{m}-a_{n}$$

Use the distributive property to multiply y by m-n.

$$ym-yn=a_{m}-a_{n}$$

Swap sides so that all variable terms are on the left hand side.

$$a_{m}-a_{n}=ym-yn$$

Subtract a_{m} from both sides.

$$-a_{n}=ym-yn-a_{m}$$

The equation is in standard form.

$$-a_{n}=my-ny-a_{m}$$

Divide both sides by -1.

$$\frac{-a_{n}}{-1}=\frac{my-ny-a_{m}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a_{n}=\frac{my-ny-a_{m}}{-1}$$

Divide ym-yn-a_{m} by -1.

$$a_{n}=ny-my+a_{m}$$

Solve for a_m

$$a_{m}=my-ny+a_{n}$$

$$m\neq n$$