Write in y=mx+b Form y-2=-5/2(x-5)

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

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

Simplify the right side.

Simplify $- \frac{5}{2} (x - 5)$ .

Apply the distributive property.

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

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

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

Multiply $- \frac{5}{2} \cdot - 5$ .

Multiply $- 5$ by $- 1$ .

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

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

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

Multiply $5$ by $5$ .

$y - 2 = - \frac{x \cdot 5}{2} + \frac{25}{2}$

Move $5$ to the left of $x$ .

$y - 2 = - \frac{5 x}{2} + \frac{25}{2}$

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

Add $2$ to both sides of the equation.

$y = - \frac{5 x}{2} + \frac{25}{2} + 2$

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

$y = - \frac{5 x}{2} + \frac{25}{2} + 2 \cdot \frac{2}{2}$

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

$y = - \frac{5 x}{2} + \frac{25}{2} + \frac{2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = - \frac{5 x}{2} + \frac{25 + 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$y = - \frac{5 x}{2} + \frac{25 + 4}{2}$

Add $25$ and $4$ .

$y = - \frac{5 x}{2} + \frac{29}{2}$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{5}{2} x) + \frac{29}{2}$

Remove parentheses.

$y = - \frac{5}{2} x + \frac{29}{2}$