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

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

Step 1

Find the x-intercepts.

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

$0 = \frac{3}{2} x - 3$

Solve the equation.

Rewrite the equation as $\frac{3}{2} x - 3 = 0$ .

$\frac{3}{2} x - 3 = 0$

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} - 3 = 0$

Add $3$ to both sides of the equation.

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

Multiply both sides of the equation by $\frac{2}{3}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 3$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot 3$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 3$

Rewrite the expression.

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

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 2$

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 $y$ .

$y = \frac{3}{2} \cdot (0) - 3$

Solve the equation.

Multiply $\frac{3}{2}$ by $0$ .

$y = \frac{3}{2} \cdot 0 - 3$

Remove parentheses.

$y = \frac{3}{2} \cdot (0) - 3$

Simplify $\frac{3}{2} \cdot (0) - 3$ .

Multiply $\frac{3}{2}$ by $0$ .

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

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

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