Find the Slope and y-intercept (-1,-16) , (0,-15)

$(- 1, - 16)$ , $(0, - 15)$

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.

$m = \frac{- 15 - (- 16)}{0 - (- 1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 16$ .

$m = \frac{- 15 + 16}{0 - (- 1)}$

Add $- 15$ and $16$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

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

Add $0$ and $1$ .

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

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, $y = m x + b$ .

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

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

$- 16 = (1) \cdot (- 1) + b$

Rewrite the equation as $(1) \cdot (- 1) + b = - 16$ .

$(1) \cdot (- 1) + b = - 16$

Multiply $- 1$ by $1$ .

$- 1 + b = - 16$

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

Add $1$ to both sides of the equation.

$b = - 16 + 1$

Add $- 16$ and $1$ .

$b = - 15$

Step 3

List the slope and y-intercept.

Slope: $1$

y-intercept: $(0, - 15)$

Step 4

Find the Slope and y-intercept (-1,-16) , (0,-15)

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