Find the Equation Using Two Points (6,-1) , (-3,2)

$(6, - 1)$ , $(- 3, 2)$

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.

$m = \frac{2 - (- 1)}{- 3 - (6)}$

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{2 + 1}{- 3 - (6)}$

Add $2$ and $1$ .

$m = \frac{3}{- 3 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{3}{- 3 - 6}$

Subtract $6$ from $- 3$ .

$m = \frac{3}{- 9}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $3$ and $- 9$ .

Factor $3$ out of $3$ .

$m = \frac{3 (1)}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

$m = \frac{3 \cdot 1}{3 \cdot - 3}$

Cancel the common factor.

$m = \frac{3 \cdot 1}{3 \cdot - 3}$

Rewrite the expression.

$m = \frac{1}{- 3}$

Move the negative in front of the fraction.

$m = - \frac{1}{3}$

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.

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

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{3}) \cdot (6) + b$

Substitute the value of $y$ into the equation.

$- 1 = (- \frac{1}{3}) \cdot (6) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{1}{3} \cdot 6 + b = - 1$ .

$- \frac{1}{3} \cdot 6 + b = - 1$

Simplify each term.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{- 1}{3} \cdot 6 + b = - 1$

Factor $3$ out of $6$ .

$\frac{- 1}{3} \cdot (3 (2)) + b = - 1$

Cancel the common factor.

$\frac{- 1}{3} \cdot (3 \cdot 2) + b = - 1$

Rewrite the expression.

$- 1 \cdot 2 + b = - 1$

Multiply $- 1$ by $2$ .

$- 2 + b = - 1$

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

Add $2$ to both sides of the equation.

$b = - 1 + 2$

Add $- 1$ and $2$ .

$b = 1$

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.

$y = - \frac{1}{3} x + 1$

Find the Equation Using Two Points (6,-1) , (-3,2)

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