Find the x and y Intercepts 2x+6y=2

$2 x + 6 y = 2$

Step 1

Find the x-intercepts.

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

$2 x + 6 (0) = 2$

Solve the equation.

Simplify $2 x + 6 (0)$ .

Multiply $6$ by $0$ .

$2 x + 0 = 2$

Add $2 x$ and $0$ .

$2 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Step 2

Find the y-intercepts.

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

$2 (0) + 6 y = 2$

Solve the equation.

Simplify $2 (0) + 6 y$ .

Multiply $2$ by $0$ .

$0 + 6 y = 2$

Add $0$ and $6 y$ .

$6 y = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$y = \frac{2 \cdot 1}{2 \cdot 3}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot 3}$

Rewrite the expression.

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

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(1, 0)$

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

Step 4

Find the x and y Intercepts 2x+6y=2

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