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

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

Step 1

Graph $x + y \geq 2$ .

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

Subtract $x$ from both sides of the inequality.

$y \geq 2 - x$

Rearrange terms.

$y \geq - x + 2$

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 $y = m x + b$ .

$m = - 1$

$b = 2$

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

Slope: $- 1$

y-intercept: $(0, 2)$

Slope: $- 1$

y-intercept: $(0, 2)$

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

$y \geq - x + 2$

Step 2

Graph $4 x + y \geq - 1$ .

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

Subtract $4 x$ from both sides of the inequality.

$y \geq - 1 - 4 x$

Rearrange terms.

$y \geq - 4 x - 1$

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 $y = m x + b$ .

$m = - 4$

$b = - 1$

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

Slope: $- 4$

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

Slope: $- 4$

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

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- 4 x - 1$ .

$y \geq - 4 x - 1$

Step 3

Plot each graph on the same coordinate system.

$x + y \geq 2$

$4 x + y \geq - 1$

Step 4

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

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