Find the x and y Intercepts f(x)=-2/9x+1/3

$f (x) = - \frac{2}{9} x + \frac{1}{3}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - \frac{2}{9} x + \frac{1}{3}$

Solve the equation.

Rewrite the equation as $- \frac{2}{9} x + \frac{1}{3} = 0$ .

$- \frac{2}{9} x + \frac{1}{3} = 0$

Simplify each term.

Combine $x$ and $\frac{2}{9}$ .

$- \frac{x \cdot 2}{9} + \frac{1}{3} = 0$

Move $2$ to the left of $x$ .

$- \frac{2 x}{9} + \frac{1}{3} = 0$

Subtract $\frac{1}{3}$ from both sides of the equation.

$- \frac{2 x}{9} = - \frac{1}{3}$

Multiply both sides of the equation by $- \frac{9}{2}$ .

$- \frac{9}{2} (- \frac{2 x}{9}) = - \frac{9}{2} (- \frac{1}{3})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{9}{2} (- \frac{2 x}{9})$ .

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$\frac{- 9}{2} (- \frac{2 x}{9}) = - \frac{9}{2} (- \frac{1}{3})$

Move the leading negative in $- \frac{2 x}{9}$ into the numerator.

$\frac{- 9}{2} \cdot \frac{- 2 x}{9} = - \frac{9}{2} (- \frac{1}{3})$

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{2} \cdot \frac{- 2 x}{9} = - \frac{9}{2} (- \frac{1}{3})$

Cancel the common factor.

$\frac{9 \cdot - 1}{2} \cdot \frac{- 2 x}{9} = - \frac{9}{2} (- \frac{1}{3})$

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{9}{2} (- \frac{1}{3})$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{9}{2} (- \frac{1}{3})$

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{9}{2} (- \frac{1}{3})$

Rewrite the expression.

$- - x = - \frac{9}{2} (- \frac{1}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{9}{2} (- \frac{1}{3})$

Multiply $x$ by $1$ .

$x = - \frac{9}{2} (- \frac{1}{3})$

Simplify the right side.

Simplify $- \frac{9}{2} (- \frac{1}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$x = \frac{- 9}{2} (- \frac{1}{3})$

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$x = \frac{- 9}{2} \cdot \frac{- 1}{3}$

Factor $3$ out of $- 9$ .

$x = \frac{3 (- 3)}{2} \cdot \frac{- 1}{3}$

Cancel the common factor.

$x = \frac{3 \cdot - 3}{2} \cdot \frac{- 1}{3}$

Rewrite the expression.

$x = \frac{- 3}{2} \cdot - 1$

Combine $\frac{- 3}{2}$ and $- 1$ .

$x = \frac{- 3 \cdot - 1}{2}$

Multiply $- 3$ by $- 1$ .

$x = \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{3}{2}, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - \frac{2}{9} \cdot 0 + \frac{1}{3}$

Solve the equation.

Remove parentheses.

$y = - \frac{2}{9} \cdot 0 + \frac{1}{3}$

Simplify $- \frac{2}{9} \cdot 0 + \frac{1}{3}$ .

Multiply $- \frac{2}{9} \cdot 0$ .

Multiply $0$ by $- 1$ .

$y = 0 (\frac{2}{9}) + \frac{1}{3}$

Multiply $0$ by $\frac{2}{9}$ .

$y = 0 + \frac{1}{3}$

Add $0$ and $\frac{1}{3}$ .

$y = \frac{1}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{3})$

Step 3

List the intersections.

x-intercept(s): $(\frac{3}{2}, 0)$

y-intercept(s): $(0, \frac{1}{3})$

Step 4

Find the x and y Intercepts f(x)=-2/9x+1/3

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