Find the Equation with a Point and Slope 1/2 , (0,9)

$\frac{1}{2}$ , $(0, 9)$

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.

$y = (\frac{1}{2}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{1}{2}) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$9 = (\frac{1}{2}) \cdot (0) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{2} \cdot 0 + b = 9$ .

$\frac{1}{2} \cdot 0 + b = 9$

Simplify $\frac{1}{2} \cdot 0 + b$ .

Multiply $\frac{1}{2}$ by $0$ .

$0 + b = 9$

Add $0$ and $b$ .

$b = 9$

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.

$y = \frac{1}{2} x + 9$

Step 3