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 $- 1$ ?

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.

Add $1$ to both sides of the equation.

$b = 5 + 1$

Add $5$ and $1$ .

$b = 6$

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.

$y = - x + 6$