Write in Slope-Intercept Form (-3,0) and (0,-3)

$(- 3, 0)$ and $(0, - 3)$

Find the slope of the line between $(- 3, 0)$ and $(0, - 3)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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.

$m = \frac{- 3 - (0)}{0 - (- 3)}$

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 3 - (0)$ and $0 - (- 3)$ .

Rewrite $- 3$ as $- 1 (3)$ .

$m = \frac{- 1 \cdot 3 - (0)}{0 - (- 3)}$

Factor $- 1$ out of $- 1 (3) - (0)$ .

$m = \frac{- 1 (3 + 0)}{0 - (- 3)}$

Reorder terms.

$m = \frac{- 1 (3 + 0)}{0 - 3 \cdot - 1}$

Factor $3$ out of $- 1 (3 + 0)$ .

$m = \frac{3 (- 1 (1 + 0))}{0 - 3 \cdot - 1}$

Cancel the common factors.

Factor $3$ out of $0$ .

$m = \frac{3 (- 1 (1 + 0))}{3 (0) - 3 \cdot - 1}$

Factor $3$ out of $- 3 \cdot - 1$ .

$m = \frac{3 (- 1 (1 + 0))}{3 (0) + 3 (1)}$

Factor $3$ out of $3 (0) + 3 (- - 1)$ .

$m = \frac{3 (- 1 (1 + 0))}{3 (0 + 1)}$

Cancel the common factor.

$m = \frac{3 (- 1 (1 + 0))}{3 (0 + 1)}$

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 $1$ .

$m = - 1$

Use the slope $- 1$ and a given point $(- 3, 0)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - 1 \cdot (x - (- 3))$

Simplify the equation and keep it in point-slope form.

$y + 0 = - 1 \cdot (x + 3)$

Solve for $y$ .

Add $y$ and $0$ .

$y = - 1 \cdot (x + 3)$

Simplify $- 1 \cdot (x + 3)$ .

Apply the distributive property.

$y = - 1 x - 1 \cdot 3$

Simplify the expression.

Rewrite $- 1 x$ as $- x$ .

$y = - x - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$y = - x - 3$

Write in Slope-Intercept Form (-3,0) and (0,-3)

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