Graph y<=x-1 x+2y>=4

$y \leq x - 1$ $x + 2 y \geq 4$

Step 1

Graph $y \leq x - 1$ .

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 $y = m x + b$ .

$m = 1$

$b = - 1$

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

Slope: $1$

y-intercept: $(0, - 1)$

Slope: $1$

y-intercept: $(0, - 1)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x - 1$ .

$y \leq x - 1$

Step 2

Graph $x + 2 y \geq 4$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y \geq 4 - x$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $4$ by $2$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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

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

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

$b = 2$

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: $(0, 2)$

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

y-intercept: $(0, 2)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x + 2$ .

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

Step 3

Plot each graph on the same coordinate system.

$y \leq x - 1$

$x + 2 y \geq 4$

Step 4

Graph y<=x-1 x+2y>=4

Related Questions

Support LCMGCF.com by disabling your adblocker.