Graph 2<=x<=6 y>=x y>=3 f(x,y)=2x-3y

$2 \leq x \leq 6$ $y \geq x$ $y \geq 3$ $f (x, y) = 2 x - 3 y$

Graph $2 \leq x \leq 6$ .

$2 \leq x \leq 6$

Graph $y \geq x$ .

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 $y = m x + b$ .

$m = 1$

$b = 0$

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

Slope: $1$

y-intercept: $(0, 0)$

Slope: $1$

y-intercept: $(0, 0)$

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

$y \geq x$

Graph $y \geq 3$ .

$y \geq 3$

Graph $f (x, y) = 2 x - 3 y$ .

Rewrite the function as an equation.

$y = 2 x - 3 y$

Move all terms containing $y$ to the left side of the equation.

Add $3 y$ to both sides of the equation.

$y + 3 y = 2 x$

Add $y$ and $3 y$ .

$4 y = 2 x$

Divide each term in $4 y = 2 x$ by $4$ and simplify.

Divide each term in $4 y = 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{2 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{2 x}{4}$

Divide $y$ by $1$ .

$y = \frac{2 x}{4}$

Simplify the right side.

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

Factor $2$ out of $2 x$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite in slope-intercept form.

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

$y = m x + b$

Reorder terms.

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

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

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

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

$b = 0$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, 0)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 0)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Write in $y = m x + b$ form.

Solve for $y$ .

Move all terms containing $y$ to the left side of the equation.

Add $3 y$ to both sides of the equation.

$y + 3 y = 2 x$

Add $y$ and $3 y$ .

$4 y = 2 x$

Divide each term in $4 y = 2 x$ by $4$ and simplify.

Divide each term in $4 y = 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{2 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{2 x}{4}$

Divide $y$ by $1$ .

$y = \frac{2 x}{4}$

Simplify the right side.

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

Factor $2$ out of $2 x$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Reorder terms.

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

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 1 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{1}{2}$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 1 \end{array}$

Slope: $\frac{1}{2}$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 1 \end{array}$

Plot each graph on the same coordinate system.

$2 \leq x \leq 6$

$y \geq x$

$y \geq 3$

$f (x, y) = 2 x - 3 y$

Graph 2<=x<=6 y>=x y>=3 f(x,y)=2x-3y

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