Find the Equation with a Point and Slope 7/9 , (0,-8/9)

$\frac{7}{9}$ , $(0, \frac{- 8}{9})$

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.

$y = (\frac{7}{9}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{7}{9}) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$\frac{- 8}{9} = (\frac{7}{9}) \cdot (0) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{7}{9} \cdot 0 + b = \frac{- 8}{9}$ .

$\frac{7}{9} \cdot 0 + b = \frac{- 8}{9}$

Simplify $\frac{7}{9} \cdot 0 + b$ .

Multiply $\frac{7}{9}$ by $0$ .

$0 + b = \frac{- 8}{9}$

Add $0$ and $b$ .

$b = \frac{- 8}{9}$

Move the negative in front of the fraction.

$b = - \frac{8}{9}$

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.

$y = \frac{7}{9} x - \frac{8}{9}$

Step 3