Find the x and y Intercepts 4x+6y=3

$4 x + 6 y = 3$

Step 1

Find the x-intercepts.

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

$4 x + 6 (0) = 3$

Solve the equation.

Simplify $4 x + 6 (0)$ .

Multiply $6$ by $0$ .

$4 x + 0 = 3$

Add $4 x$ and $0$ .

$4 x = 3$

Divide each term in $4 x = 3$ by $4$ and simplify.

Divide each term in $4 x = 3$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4}$

Divide $x$ by $1$ .

$x = \frac{3}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{3}{4}, 0)$

Step 2

Find the y-intercepts.

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

$4 (0) + 6 y = 3$

Solve the equation.

Simplify $4 (0) + 6 y$ .

Multiply $4$ by $0$ .

$0 + 6 y = 3$

Add $0$ and $6 y$ .

$6 y = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$y = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$y = \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$y = \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

$y = \frac{1}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{2})$

Step 3

List the intersections.

x-intercept(s): $(\frac{3}{4}, 0)$

y-intercept(s): $(0, \frac{1}{2})$

Step 4

Find the x and y Intercepts 4x+6y=3

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