Find the Equation Using Slope-Intercept Form (2,-3) , y=4x-9

$(2, - 3)$ , $y = 4 x - 9$

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.

$y = (4 x - 9) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (4 (2) - 9) \cdot (2) + b$

Substitute the value of $y$ into the equation.

$- 3 = (4 (2) - 9) \cdot (2) + b$

Find the value of $b$ .

Rewrite the equation as $(4 (2) - 9) \cdot 2 + b = - 3$ .

$(4 (2) - 9) \cdot 2 + b = - 3$

Simplify each term.

Multiply $4$ by $2$ .

$(8 - 9) \cdot 2 + b = - 3$

Subtract $9$ from $8$ .

$- 1 \cdot 2 + b = - 3$

Multiply $- 1$ by $2$ .

$- 2 + b = - 3$

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

Add $2$ to both sides of the equation.

$b = - 3 + 2$

Add $- 3$ and $2$ .

$b = - 1$

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.

$y = 4 x^{2} - 9 x - 1$

Step 3