Find the x and y Intercepts 2x+3y-6=0

$2 x + 3 y - 6 = 0$

Step 1

Find the x-intercepts.

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

$2 x + 3 (0) - 6 = 0$

Solve the equation.

Simplify $2 x + 3 (0) - 6$ .

Multiply $3$ by $0$ .

$2 x + 0 - 6 = 0$

Add $2 x$ and $0$ .

$2 x - 6 = 0$

Add $6$ to both sides of the equation.

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$2 (0) + 3 y - 6 = 0$

Solve the equation.

Simplify $2 (0) + 3 y - 6$ .

Multiply $2$ by $0$ .

$0 + 3 y - 6 = 0$

Add $0$ and $3 y$ .

$3 y - 6 = 0$

Add $6$ to both sides of the equation.

$3 y = 6$

Divide each term in $3 y = 6$ by $3$ and simplify.

Divide each term in $3 y = 6$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3}$

Divide $y$ by $1$ .

$y = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 2)$

Step 4

Find the x and y Intercepts 2x+3y-6=0

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