Find the Equation with a Point and Slope (10,2) ; 12

$(10, 2)$ ; $12$

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.

$y = (12) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (12) \cdot (10) + b$

Substitute the value of $y$ into the equation.

$2 = (12) \cdot (10) + b$

Find the value of $b$ .

Rewrite the equation as $(12) \cdot (10) + b = 2$ .

$(12) \cdot (10) + b = 2$

Multiply $12$ by $10$ .

$120 + b = 2$

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

Subtract $120$ from both sides of the equation.

$b = 2 - 120$

Subtract $120$ from $2$ .

$b = - 118$

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.

$y = 12 x - 118$

Step 3