Find the Slope and y-intercept (-6,0) , (0,6)

$(- 6, 0)$ , $(0, 6)$

Step 1

Find the value of the slope.

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.

$m = \frac{6 - (0)}{0 - (- 6)}$

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $6 - (0)$ and $0 - (- 6)$ .

Rewrite $6$ as $- 1 (- 6)$ .

$m = \frac{- 1 \cdot - 6 - (0)}{0 - (- 6)}$

Factor $- 1$ out of $- 1 (- 6) - (0)$ .

$m = \frac{- 1 (- 6 + 0)}{0 - (- 6)}$

Reorder terms.

$m = \frac{- 1 (- 6 + 0)}{0 - 6 \cdot - 1}$

Factor $6$ out of $- 1 (- 6 + 0)$ .

$m = \frac{6 (- 1 (- 1 + 0))}{0 - 6 \cdot - 1}$

Cancel the common factors.

Factor $6$ out of $0$ .

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0) - 6 \cdot - 1}$

Factor $6$ out of $- 6 \cdot - 1$ .

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0) + 6 (1)}$

Factor $6$ out of $6 (0) + 6 (- - 1)$ .

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0 + 1)}$

Cancel the common factor.

$m = \frac{6 (- 1 (- 1 + 0))}{6 (0 + 1)}$

Rewrite the expression.

$m = \frac{- 1 (- 1 + 0)}{0 + 1}$

Add $- 1$ and $0$ .

$m = \frac{- 1 \cdot - 1}{0 + 1}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$m = \frac{- 1 \cdot - 1}{0 + 1}$

Add $0$ and $1$ .

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

Simplify the expression.

Multiply $- 1$ by $- 1$ .

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

Divide $1$ by $1$ .

$m = 1$

Step 2

Find the value of the y-intercept.

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (1) \cdot x + b$

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (1) \cdot (- 6) + b$

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$0 = (1) \cdot (- 6) + b$

Rewrite the equation as $(1) \cdot (- 6) + b = 0$ .

$(1) \cdot (- 6) + b = 0$

Multiply $- 6$ by $1$ .

$- 6 + b = 0$

Add $6$ to both sides of the equation.

$b = 6$

Step 3

List the slope and y-intercept.

Slope: $1$

y-intercept: $(0, 6)$

Step 4

Find the Slope and y-intercept (-6,0) , (0,6)

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