Find the Equation with a Point and Slope (1,-1) , 4/3

$(1, - 1)$ , $\frac{4}{3}$

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.

$y = (\frac{4}{3}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{4}{3}) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$- 1 = (\frac{4}{3}) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{4}{3} \cdot 1 + b = - 1$ .

$\frac{4}{3} \cdot 1 + b = - 1$

Multiply $\frac{4}{3}$ by $1$ .

$\frac{4}{3} + b = - 1$

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

Subtract $\frac{4}{3}$ from both sides of the equation.

$b = - 1 - \frac{4}{3}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - 1 \cdot \frac{3}{3} - \frac{4}{3}$

Combine $- 1$ and $\frac{3}{3}$ .

$b = \frac{- 1 \cdot 3}{3} - \frac{4}{3}$

Combine the numerators over the common denominator.

$b = \frac{- 1 \cdot 3 - 4}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$b = \frac{- 3 - 4}{3}$

Subtract $4$ from $- 3$ .

$b = \frac{- 7}{3}$

Move the negative in front of the fraction.

$b = - \frac{7}{3}$

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.

$y = \frac{4}{3} x - \frac{7}{3}$

Step 3