Find the Equation Using Point-Slope Formula (0,0) , (-1/8,1/9)

$(0, 0)$ , $(- \frac{1}{8}, \frac{1}{9})$

Step 1

Find the slope of the line between $(0, 0)$ and $(- \frac{1}{8}, \frac{1}{9})$ 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.

$m = \frac{\frac{1}{9} - (0)}{- \frac{1}{8} - (0)}$

Simplify.

Multiply the numerator and denominator of the complex fraction by $72$ .

Multiply $\frac{\frac{1}{9} - (0)}{- \frac{1}{8} - (0)}$ by $\frac{72}{72}$ .

$m = \frac{72}{72} \cdot \frac{\frac{1}{9} - (0)}{- \frac{1}{8} - (0)}$

Combine.

$m = \frac{72 (\frac{1}{9} - (0))}{72 (- \frac{1}{8} - (0))}$

Apply the distributive property.

$m = \frac{72 (\frac{1}{9}) + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Simplify by cancelling.

Cancel the common factor of $9$ .

Factor $9$ out of $72$ .

$m = \frac{9 (8) (\frac{1}{9}) + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Cancel the common factor.

$m = \frac{9 \cdot (8 (\frac{1}{9})) + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Rewrite the expression.

$m = \frac{8 + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$m = \frac{8 + 72 (- (0))}{72 (\frac{- 1}{8}) + 72 (- (0))}$

Factor $8$ out of $72$ .

$m = \frac{8 + 72 (- (0))}{8 (9) (\frac{- 1}{8}) + 72 (- (0))}$

Cancel the common factor.

$m = \frac{8 + 72 (- (0))}{8 \cdot (9 (\frac{- 1}{8})) + 72 (- (0))}$

Rewrite the expression.

$m = \frac{8 + 72 (- (0))}{9 \cdot - 1 + 72 (- (0))}$

Multiply $9$ by $- 1$ .

$m = \frac{8 + 72 (- (0))}{- 9 + 72 (- (0))}$

Simplify the numerator.

Multiply $72 (- (0))$ .

Multiply $- 1$ by $0$ .

$m = \frac{8 + 72 \cdot 0}{- 9 + 72 (- (0))}$

Multiply $72$ by $0$ .

$m = \frac{8 + 0}{- 9 + 72 (- (0))}$

Add $8$ and $0$ .

$m = \frac{8}{- 9 + 72 (- (0))}$

Simplify the denominator.

Multiply $72 (- (0))$ .

Multiply $- 1$ by $0$ .

$m = \frac{8}{- 9 + 72 \cdot 0}$

Multiply $72$ by $0$ .

$m = \frac{8}{- 9 + 0}$

Add $- 9$ and $0$ .

$m = \frac{8}{- 9}$

Move the negative in front of the fraction.

$m = - \frac{8}{9}$

Step 2

Use the slope $- \frac{8}{9}$ and a given point $(0, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{8}{9} \cdot (x - (0))$

Step 3

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

$y + 0 = - \frac{8}{9} \cdot (x + 0)$

Step 4

Solve for $y$ .

Add $y$ and $0$ .

$y = - \frac{8}{9} \cdot (x + 0)$

Simplify $- \frac{8}{9} \cdot (x + 0)$ .

Add $x$ and $0$ .

$y = - \frac{8}{9} \cdot x$

Combine $x$ and $\frac{8}{9}$ .

$y = - \frac{x \cdot 8}{9}$

Move $8$ to the left of $x$ .

$y = - \frac{8 x}{9}$

Step 5

Reorder terms.

$y = - (\frac{8}{9} x)$

Step 6

Remove parentheses.

$y = - \frac{8}{9} x$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{8}{9} x$

Point-slope form:

$y + 0 = - \frac{8}{9} \cdot (x + 0)$

Step 8

Find the Equation Using Point-Slope Formula (0,0) , (-1/8,1/9)

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