Write in Slope-Intercept Form (4,-3) , y=3x-5

$(4, - 3)$ , $y = 3 x - 5$

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.

$y = (3 x - 5) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (3 (4) - 5) \cdot (4) + b$

Substitute the value of $y$ into the equation.

$- 3 = (3 (4) - 5) \cdot (4) + b$

Find the value of $b$ .

Rewrite the equation as $(3 (4) - 5) \cdot 4 + b = - 3$ .

$(3 (4) - 5) \cdot 4 + b = - 3$

Simplify each term.

Multiply $3$ by $4$ .

$(12 - 5) \cdot 4 + b = - 3$

Subtract $5$ from $12$ .

$7 \cdot 4 + b = - 3$

Multiply $7$ by $4$ .

$28 + b = - 3$

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

Subtract $28$ from both sides of the equation.

$b = - 3 - 28$

Subtract $28$ from $- 3$ .

$b = - 31$

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.

$y = 3 x^{2} - 5 x - 31$

Step 3