Find the Slope and y-intercept (-5,0) , (0,-1)

$(- 5, 0)$ , $(0, - 1)$

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.

$m = \frac{- 1 - (0)}{0 - (- 5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{- 1 + 0}{0 - (- 5)}$

Add $- 1$ and $0$ .

$m = \frac{- 1}{0 - (- 5)}$

Simplify the denominator.

Multiply $- 1$ by $- 5$ .

$m = \frac{- 1}{0 + 5}$

Add $0$ and $5$ .

$m = \frac{- 1}{5}$

Move the negative in front of the fraction.

$m = - \frac{1}{5}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{1}{5}) \cdot x + b$

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

$y = (- \frac{1}{5}) \cdot (- 5) + b$

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

$0 = (- \frac{1}{5}) \cdot (- 5) + b$

Rewrite the equation as $(- \frac{1}{5}) \cdot (- 5) + b = 0$ .

$(- \frac{1}{5}) \cdot (- 5) + b = 0$

Simplify each term.

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{- 1}{5} \cdot - 5 + b = 0$

Factor $5$ out of $- 5$ .

$\frac{- 1}{5} \cdot (5 (- 1)) + b = 0$

Cancel the common factor.

$\frac{- 1}{5} \cdot (5 \cdot - 1) + b = 0$

Rewrite the expression.

$- 1 \cdot - 1 + b = 0$

Multiply $- 1$ by $- 1$ .

$1 + b = 0$

Subtract $1$ from both sides of the equation.

$b = - 1$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{5}$

y-intercept: $(0, - 1)$

Step 4

Find the Slope and y-intercept (-5,0) , (0,-1)

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