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

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

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.

$y = (2 x) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Multiply $2 (3) \cdot 3$ .

Multiply $2$ by $3$ .

$6 \cdot 3 + b = 4$

Multiply $6$ by $3$ .

$18 + b = 4$

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

Subtract $18$ from both sides of the equation.

$b = 4 - 18$

Subtract $18$ from $4$ .

$b = - 14$

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.

$y = 2 x^{2} - 14$

Step 3