Find the x and y Intercepts y=3x-2

$y = 3 x - 2$

Step 1

Find the x-intercepts.

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

$0 = 3 x - 2$

Solve the equation.

Rewrite the equation as $3 x - 2 = 0$ .

$3 x - 2 = 0$

Add $2$ to both sides of the equation.

$3 x = 2$

Divide each term in $3 x = 2$ by $3$ and simplify.

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Divide $x$ by $1$ .

$x = \frac{2}{3}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{2}{3}, 0)$

Step 2

Find the y-intercepts.

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

$y = 3 (0) - 2$

Solve the equation.

Remove parentheses.

$y = 3 (0) - 2$

Simplify $3 (0) - 2$ .

Multiply $3$ by $0$ .

$y = 0 - 2$

Subtract $2$ from $0$ .

$y = - 2$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{2}{3}, 0)$

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

Step 4