Find the Equation Using Two Points (-10,3) , (-8,-8)

$(- 10, 3)$ , $(- 8, - 8)$

Step 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.

Step 2

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

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

Step 3

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).

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

Step 4

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

$m = \frac{- 8 - (3)}{- 8 - (- 10)}$

Step 5

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $3$ .

$m = \frac{- 8 - 3}{- 8 - (- 10)}$

Subtract $3$ from $- 8$ .

$m = \frac{- 11}{- 8 - (- 10)}$

Simplify the denominator.

Multiply $- 1$ by $- 10$ .

$m = \frac{- 11}{- 8 + 10}$

Add $- 8$ and $10$ .

$m = \frac{- 11}{2}$

Move the negative in front of the fraction.

$m = - \frac{11}{2}$

Step 6

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.

$y = (- \frac{11}{2}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{11}{2}) \cdot (- 10) + b$

Substitute the value of $y$ into the equation.

$3 = (- \frac{11}{2}) \cdot (- 10) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{11}{2} \cdot - 10 + b = 3$ .

$- \frac{11}{2} \cdot - 10 + b = 3$

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{11}{2}$ into the numerator.

$\frac{- 11}{2} \cdot - 10 + b = 3$

Factor $2$ out of $- 10$ .

$\frac{- 11}{2} \cdot (2 (- 5)) + b = 3$

Cancel the common factor.

$\frac{- 11}{2} \cdot (2 \cdot - 5) + b = 3$

Rewrite the expression.

$- 11 \cdot - 5 + b = 3$

Multiply $- 11$ by $- 5$ .

$55 + b = 3$

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

Subtract $55$ from both sides of the equation.

$b = 3 - 55$

Subtract $55$ from $3$ .

$b = - 52$

Step 7

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.

$y = - \frac{11}{2} x - 52$

Step 8

Find the Equation Using Two Points (-10,3) , (-8,-8)

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