Find the Equation with a Point and Slope (-1/2,1/2) , -1

$(- \frac{1}{2}, \frac{1}{2})$ , $- 1$

Step 1

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (- 1) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 1) \cdot (- \frac{1}{2}) + b$

Substitute the value of $y$ into the equation.

$\frac{1}{2} = (- 1) \cdot (- \frac{1}{2}) + b$

Find the value of $b$ .

Rewrite the equation as $- 1 \cdot (- 1 (\frac{1}{2})) + b = \frac{1}{2}$ .

$- 1 \cdot (- 1 (\frac{1}{2})) + b = \frac{1}{2}$

Simplify each term.

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

$- 1 \cdot (- (\frac{1}{2})) + b = \frac{1}{2}$

Multiply $- 1 (- \frac{1}{2})$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{1}{2}) + b = \frac{1}{2}$

Multiply $\frac{1}{2}$ by $1$ .

$\frac{1}{2} + b = \frac{1}{2}$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$b = \frac{1}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$b = \frac{1 - 1}{2}$

Subtract $1$ from $1$ .

$b = \frac{0}{2}$

Divide $0$ by $2$ .

$b = 0$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - x$

Step 3