Find the Equation Using Point-Slope Formula (-1,-16) , (0,-15)

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

Step 1

Find the slope of the line between $(- 1, - 16)$ and $(0, - 15)$ 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.

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

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

Use the slope $1$ and a given point $(- 1, - 16)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 16) = 1 \cdot (x - (- 1))$

Step 3

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

$y + 16 = 1 \cdot (x + 1)$

Step 4

Solve for $y$ .

Multiply $x + 1$ by $1$ .

$y + 16 = x + 1$

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

Subtract $16$ from both sides of the equation.

$y = x + 1 - 16$

Subtract $16$ from $1$ .

$y = x - 15$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = x - 15$

Point-slope form:

$y + 16 = 1 \cdot (x + 1)$

Step 6

Find the Equation Using Point-Slope Formula (-1,-16) , (0,-15)

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