Graph y<-x 3 y>=2x-1

$y < - x$ $3$ $y \geq 2 x - 1$

Step 1

Graph $y < - x$ .

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 dashed line, then shade the area below the boundary line since $y$ is less than $- x$ .

$y < - x$

Step 2

Graph $3$ .

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 $y = m x + b$ .

$m = 0$

$b = 3$

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

Slope: $0$

y-intercept: $(0, 3)$

Slope: $0$

y-intercept: $(0, 3)$

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 3 \end{array}$

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

Slope: $0$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 3 \end{array}$

Slope: $0$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 3 \end{array}$

Step 3

Graph $y \geq 2 x - 1$ .

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 $y = m x + b$ .

$m = 2$

$b = - 1$

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

Slope: $2$

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

Slope: $2$

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

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

$y \geq 2 x - 1$

Step 4

Plot each graph on the same coordinate system.

$y < - x$

$3$

$y \geq 2 x - 1$

Step 5

Graph y<-x 3 y>=2x-1

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