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

$y = 3 x - 6$

Find the x-intercepts.

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

$0 = 3 x - 6$

Solve the equation.

Rewrite the equation as $3 x - 6 = 0$ .

$3 x - 6 = 0$

Add $6$ to both sides of the equation.

$3 x = 6$

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): $(2, 0)$

Find the y-intercepts.

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

$y = 3 (0) - 6$

Solve the equation.

Remove parentheses.

$y = 3 (0) - 6$

Simplify $3 (0) - 6$ .

Multiply $3$ by $0$ .

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

y-intercept(s) in point form.

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

List the intersections.

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

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