Find the Equation with a Point and Slope -3 , (1,3)

$- 3$ , $(1, 3)$

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.

$y = (- 3) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 3) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$3 = (- 3) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $(- 3) \cdot (1) + b = 3$ .

$(- 3) \cdot (1) + b = 3$

Multiply $- 3$ by $1$ .

$- 3 + b = 3$

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

Add $3$ to both sides of the equation.

$b = 3 + 3$

Add $3$ and $3$ .

$b = 6$

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.

$y = - 3 x + 6$

Step 3