Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-1,-5) and has a slope of -1 ?

What is the equation of the line that passes through the point $(- 1, - 5)$ and has a slope of $- 1$ ?

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.

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

Substitute the value of $y$ into the equation.

$- 5 = (- 1) \cdot (- 1) + b$

Find the value of $b$ .

Rewrite the equation as $(- 1) \cdot (- 1) + b = - 5$ .

$(- 1) \cdot (- 1) + b = - 5$

Multiply $- 1$ by $- 1$ .

$1 + b = - 5$

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

Subtract $1$ from both sides of the equation.

$b = - 5 - 1$

Subtract $1$ from $- 5$ .

$b = - 6$

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.

$y = - x - 6$

Step 3