Find the Equation with a Point and Slope (8,3) ; m=6

$(8, 3)$ ; $m = 6$

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.

$y = (6) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (6) \cdot (8) + b$

Substitute the value of $y$ into the equation.

$3 = (6) \cdot (8) + b$

Find the value of $b$ .

Rewrite the equation as $(6) \cdot (8) + b = 3$ .

$(6) \cdot (8) + b = 3$

Multiply $6$ by $8$ .

$48 + b = 3$

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

Subtract $48$ from both sides of the equation.

$b = 3 - 48$

Subtract $48$ from $3$ .

$b = - 45$

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.

$y = 6 x - 45$