Find the Equation Using Slope-Intercept Form y=3x+6 , (4,7)

$y = 3 x + 6$ , $(4, 7)$

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.

$y = (3 x + 6) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (3 (4) + 6) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$7 = (3 (4) + 6) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $(3 (4) + 6) \cdot 4 + b = 7$ .

$(3 (4) + 6) \cdot 4 + b = 7$

Simplify each term.

Multiply $3$ by $4$ .

$(12 + 6) \cdot 4 + b = 7$

Add $12$ and $6$ .

$18 \cdot 4 + b = 7$

Multiply $18$ by $4$ .

$72 + b = 7$

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

Subtract $72$ from both sides of the equation.

$b = 7 - 72$

Subtract $72$ from $7$ .

$b = - 65$

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.

$y = 3 x^{2} + 6 x - 65$