Find the x and y Intercepts 2x-3y=9

$2 x - 3 y = 9$

Step 1

Find the x-intercepts.

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

$2 x - 3 \cdot 0 = 9$

Solve the equation.

Simplify $2 x - 3 \cdot 0$ .

Multiply $- 3$ by $0$ .

$2 x + 0 = 9$

Add $2 x$ and $0$ .

$2 x = 9$

Divide each term in $2 x = 9$ by $2$ and simplify.

Divide each term in $2 x = 9$ by $2$ .

$\frac{2 x}{2} = \frac{9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{9}{2}$

Divide $x$ by $1$ .

$x = \frac{9}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{9}{2}, 0)$

Step 2

Find the y-intercepts.

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

$2 (0) - 3 y = 9$

Solve the equation.

Simplify $2 (0) - 3 y$ .

Multiply $2$ by $0$ .

$0 - 3 y = 9$

Subtract $3 y$ from $0$ .

$- 3 y = 9$

Divide each term in $- 3 y = 9$ by $- 3$ and simplify.

Divide each term in $- 3 y = 9$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{9}{- 3}$

Divide $y$ by $1$ .

$y = \frac{9}{- 3}$

Simplify the right side.

Divide $9$ by $- 3$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

x-intercept(s): $(\frac{9}{2}, 0)$

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts 2x-3y=9

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