Find the Equation Using Two Points (-6,24) , (5,-31)

$(- 6, 24)$ , $(5, - 31)$

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.

$m = \frac{- 31 - (24)}{5 - (- 6)}$

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $24$ .

$m = \frac{- 31 - 24}{5 - (- 6)}$

Subtract $24$ from $- 31$ .

$m = \frac{- 55}{5 - (- 6)}$

Simplify the denominator.

Multiply $- 1$ by $- 6$ .

$m = \frac{- 55}{5 + 6}$

Add $5$ and $6$ .

$m = \frac{- 55}{11}$

Divide $- 55$ by $11$ .

$m = - 5$

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.

$y = (- 5) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 5) \cdot (- 6) + b$

Substitute the value of $y$ into the equation.

$24 = (- 5) \cdot (- 6) + b$

Find the value of $b$ .

Rewrite the equation as $(- 5) \cdot (- 6) + b = 24$ .

$(- 5) \cdot (- 6) + b = 24$

Multiply $- 5$ by $- 6$ .

$30 + b = 24$

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

Subtract $30$ from both sides of the equation.

$b = 24 - 30$

Subtract $30$ from $24$ .

$b = - 6$

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.

$y = - 5 x - 6$

Find the Equation Using Two Points (-6,24) , (5,-31)

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