Find the Equation Using Slope-Intercept Form (3,2) , y=x+5

$(3, 2)$ , $y = x + 5$

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$2 = ((3) + 5) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(3 + 5) \cdot 3 + b = 2$ .

$(3 + 5) \cdot 3 + b = 2$

Simplify each term.

Add $3$ and $5$ .

$8 \cdot 3 + b = 2$

Multiply $8$ by $3$ .

$24 + b = 2$

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

Subtract $24$ from both sides of the equation.

$b = 2 - 24$

Subtract $24$ from $2$ .

$b = - 22$

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.

$y = x^{2} + 5 x - 22$

Step 3