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

$3 x + y > 1$ $y \leq x + 2$

Step 1

Graph $3 x + y > 1$ .

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

Subtract $3 x$ from both sides of the inequality.

$y > 1 - 3 x$

Rearrange terms.

$y > - 3 x + 1$

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 $y = m x + b$ .

$m = - 3$

$b = 1$

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

Slope: $- 3$

y-intercept: $(0, 1)$

Slope: $- 3$

y-intercept: $(0, 1)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- 3 x + 1$ .

$y > - 3 x + 1$

Step 2

Graph $y \leq x + 2$ .

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 below the boundary line since $y$ is less than $x + 2$ .

$y \leq x + 2$

Step 3

Plot each graph on the same coordinate system.

$3 x + y > 1$

$y \leq x + 2$

Step 4