Find the x and y Intercepts 4x+2y=6

$4 x + 2 y = 6$

Step 1

Find the x-intercepts.

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

$4 x + 2 (0) = 6$

Solve the equation.

Simplify $4 x + 2 (0)$ .

Multiply $2$ by $0$ .

$4 x + 0 = 6$

Add $4 x$ and $0$ .

$4 x = 6$

Divide each term in $4 x = 6$ by $4$ and simplify.

Divide each term in $4 x = 6$ by $4$ .

$\frac{4 x}{4} = \frac{6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{6}{4}$

Divide $x$ by $1$ .

$x = \frac{6}{4}$

Simplify the right side.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$4 (0) + 2 y = 6$

Solve the equation.

Simplify $4 (0) + 2 y$ .

Multiply $4$ by $0$ .

$0 + 2 y = 6$

Add $0$ and $2 y$ .

$2 y = 6$

Divide each term in $2 y = 6$ by $2$ and simplify.

Divide each term in $2 y = 6$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$y = 3$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts 4x+2y=6

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