Find the Equation Using Slope-Intercept Form (0,2) , m=5/6

$(0, 2)$ , $m = \frac{5}{6}$

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.

$y = (\frac{5}{6}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{5}{6}) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$2 = (\frac{5}{6}) \cdot (0) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{5}{6} \cdot 0 + b = 2$ .

$\frac{5}{6} \cdot 0 + b = 2$

Simplify $\frac{5}{6} \cdot 0 + b$ .

Multiply $\frac{5}{6}$ by $0$ .

$0 + b = 2$

Add $0$ and $b$ .

$b = 2$

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.

$y = \frac{5}{6} x + 2$