Find the x and y Intercepts 6y=3+x

$6 y = 3 + x$

Find the x-intercepts.

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

$6 (0) = 3 + x$

Solve the equation.

Rewrite the equation as $3 + x = 6 (0)$ .

$3 + x = 6 (0)$

Multiply $6$ by $0$ .

$3 + x = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$6 y = 3 + 0$

Solve the equation.

Add $3$ and $0$ .

$6 y = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$y = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{2})$

List the intersections.

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

y-intercept(s): $(0, \frac{1}{2})$