Solve for y y-5=(7/8)(x-4)

$y - 5 = (\frac{7}{8}) (x - 4)$

Step 1

Simplify $\frac{7}{8} \cdot (x - 4)$ .

Rewrite.

$y - 5 = 0 + 0 + \frac{7}{8} \cdot (x - 4)$

Simplify by adding zeros.

$y - 5 = \frac{7}{8} \cdot (x - 4)$

Apply the distributive property.

$y - 5 = \frac{7}{8} x + \frac{7}{8} \cdot - 4$

Combine $\frac{7}{8}$ and $x$ .

$y - 5 = \frac{7 x}{8} + \frac{7}{8} \cdot - 4$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$y - 5 = \frac{7 x}{8} + \frac{7}{4 (2)} \cdot - 4$

Factor $4$ out of $- 4$ .

$y - 5 = \frac{7 x}{8} + \frac{7}{4 \cdot 2} \cdot (4 \cdot - 1)$

Cancel the common factor.

$y - 5 = \frac{7 x}{8} + \frac{7}{4 \cdot 2} \cdot (4 \cdot - 1)$

Rewrite the expression.

$y - 5 = \frac{7 x}{8} + \frac{7}{2} \cdot - 1$

Combine $\frac{7}{2}$ and $- 1$ .

$y - 5 = \frac{7 x}{8} + \frac{7 \cdot - 1}{2}$

Simplify the expression.

Multiply $7$ by $- 1$ .

$y - 5 = \frac{7 x}{8} + \frac{- 7}{2}$

Move the negative in front of the fraction.

$y - 5 = \frac{7 x}{8} - \frac{7}{2}$

Step 2

Move all terms not containing $y$ to the right side of the equation.

Add $5$ to both sides of the equation.

$y = \frac{7 x}{8} - \frac{7}{2} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{7 x}{8} - \frac{7}{2} + 5 \cdot \frac{2}{2}$

Combine $5$ and $\frac{2}{2}$ .

$y = \frac{7 x}{8} - \frac{7}{2} + \frac{5 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{7 x}{8} + \frac{- 7 + 5 \cdot 2}{2}$

Simplify the numerator.

Multiply $5$ by $2$ .

$y = \frac{7 x}{8} + \frac{- 7 + 10}{2}$

Add $- 7$ and $10$ .

$y = \frac{7 x}{8} + \frac{3}{2}$