Solve y-1=5/2(x-2)

$$y - 1 = \frac { 5 } { 2 } ( x - 2 )$$

Solve for x

$$x=\frac{2\left(y+4\right)}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{2} by x-2.

$$y-1=\frac{5}{2}x-5$$

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

$$\frac{5}{2}x-5=y-1$$

Add 5 to both sides.

$$\frac{5}{2}x=y-1+5$$

Add -1 and 5 to get 4.

$$\frac{5}{2}x=y+4$$

Divide both sides of the equation by \frac{5}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{2}x}{\frac{5}{2}}=\frac{y+4}{\frac{5}{2}}$$

Dividing by \frac{5}{2} undoes the multiplication by \frac{5}{2}.

$$x=\frac{y+4}{\frac{5}{2}}$$

Divide y+4 by \frac{5}{2} by multiplying y+4 by the reciprocal of \frac{5}{2}.

$$x=\frac{2y+8}{5}$$

Solve for y

$$y=\frac{5x}{2}-4$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by x-2.

$$y-1=\frac{5}{2}x-5$$

Add 1 to both sides.

$$y=\frac{5}{2}x-5+1$$

Add -5 and 1 to get -4.

$$y=\frac{5}{2}x-4$$