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

$3 x + y = 6$

Step 1

Find the x-intercepts.

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

$3 x + 0 = 6$

Solve the equation.

Add $3 x$ and $0$ .

$3 x = 6$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$3 (0) + y = 6$

Simplify $3 (0) + y$ .

Multiply $3$ by $0$ .

$0 + y = 6$

Add $0$ and $y$ .

$y = 6$

y-intercept(s) in point form.

y-intercept(s): $(0, 6)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 6)$

Step 4