Find the x and y Intercepts 6y-3x=27

$6 y - 3 x = 27$

Step 1

Find the x-intercepts.

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

$6 (0) - 3 x = 27$

Solve the equation.

Simplify $6 (0) - 3 x$ .

Multiply $6$ by $0$ .

$0 - 3 x = 27$

Subtract $3 x$ from $0$ .

$- 3 x = 27$

Divide each term in $- 3 x = 27$ by $- 3$ and simplify.

Divide each term in $- 3 x = 27$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{27}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{27}{- 3}$

Divide $x$ by $1$ .

$x = \frac{27}{- 3}$

Simplify the right side.

Divide $27$ by $- 3$ .

$x = - 9$

x-intercept(s) in point form.

x-intercept(s): $(- 9, 0)$

Step 2

Find the y-intercepts.

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

$6 y - 3 \cdot 0 = 27$

Solve the equation.

Simplify $6 y - 3 \cdot 0$ .

Multiply $- 3$ by $0$ .

$6 y + 0 = 27$

Add $6 y$ and $0$ .

$6 y = 27$

Divide each term in $6 y = 27$ by $6$ and simplify.

Divide each term in $6 y = 27$ by $6$ .

$\frac{6 y}{6} = \frac{27}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{27}{6}$

Divide $y$ by $1$ .

$y = \frac{27}{6}$

Simplify the right side.

Cancel the common factor of $27$ and $6$ .

Factor $3$ out of $27$ .

$y = \frac{3 (9)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$y = \frac{3 \cdot 9}{3 \cdot 2}$

Cancel the common factor.

$y = \frac{3 \cdot 9}{3 \cdot 2}$

Rewrite the expression.

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

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- 9, 0)$

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

Step 4

Find the x and y Intercepts 6y-3x=27

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