Find the Equation Using Two Points (1,-6) and (-8,-1)

$(1, - 6)$ and $(- 8, - 1)$

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{(change in y)}{(change in x)}$

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 1 - (- 6)}{- 8 - (1)}$

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $- 6$ .

$m = \frac{- 1 + 6}{- 8 - (1)}$

Add $- 1$ and $6$ .

$m = \frac{5}{- 8 - (1)}$

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{5}{- 8 - 1}$

Subtract $1$ from $- 8$ .

$m = \frac{5}{- 9}$

Move the negative in front of the fraction.

$m = - \frac{5}{9}$

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.

$y = (- \frac{5}{9}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{5}{9}) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$- 6 = (- \frac{5}{9}) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{5}{9} \cdot 1 + b = - 6$ .

$- \frac{5}{9} \cdot 1 + b = - 6$

Multiply $- 1$ by $1$ .

$- \frac{5}{9} + b = - 6$

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

Add $\frac{5}{9}$ to both sides of the equation.

$b = - 6 + \frac{5}{9}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$b = - 6 \cdot \frac{9}{9} + \frac{5}{9}$

Combine $- 6$ and $\frac{9}{9}$ .

$b = \frac{- 6 \cdot 9}{9} + \frac{5}{9}$

Combine the numerators over the common denominator.

$b = \frac{- 6 \cdot 9 + 5}{9}$

Simplify the numerator.

Multiply $- 6$ by $9$ .

$b = \frac{- 54 + 5}{9}$

Add $- 54$ and $5$ .

$b = \frac{- 49}{9}$

Move the negative in front of the fraction.

$b = - \frac{49}{9}$

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.

$y = - \frac{5}{9} x - \frac{49}{9}$

Find the Equation Using Two Points (1,-6) and (-8,-1)

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