Graph 2y>=4x-6

$2 y \geq 4 x - 6$

Step 1

Divide each term in $2 y \geq 4 x - 6$ by $2$ and simplify.

Divide each term in $2 y \geq 4 x - 6$ by $2$ .

$\frac{2 y}{2} \geq \frac{4 x}{2} + \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \geq \frac{4 x}{2} + \frac{- 6}{2}$

Divide $y$ by $1$ .

$y \geq \frac{4 x}{2} + \frac{- 6}{2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x$ .

$y \geq \frac{2 (2 x)}{2} + \frac{- 6}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y \geq \frac{2 (2 x)}{2 (1)} + \frac{- 6}{2}$

Cancel the common factor.

$y \geq \frac{2 (2 x)}{2 \cdot 1} + \frac{- 6}{2}$

Rewrite the expression.

$y \geq \frac{2 x}{1} + \frac{- 6}{2}$

Divide $2 x$ by $1$ .

$y \geq 2 x + \frac{- 6}{2}$

Divide $- 6$ by $2$ .

$y \geq 2 x - 3$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 2$

$b = - 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $2$

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

Slope: $2$

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

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $2 x - 3$ .

$y \geq 2 x - 3$

Step 4