Find the Equation with a Point and Slope (4,5) , -5

$(4, 5)$ , $- 5$

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.

$y = (- 5) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 5) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$5 = (- 5) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $(- 5) \cdot (4) + b = 5$ .

$(- 5) \cdot (4) + b = 5$

Multiply $- 5$ by $4$ .

$- 20 + b = 5$

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

Add $20$ to both sides of the equation.

$b = 5 + 20$

Add $5$ and $20$ .

$b = 25$

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.

$y = - 5 x + 25$

Step 3