Graph 3x-2<=5x+y

$3 x - 2 \leq 5 x + y$

Step 1

Solve for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$5 x + y \geq 3 x - 2$

Move all terms not containing $y$ to the right side of the inequality.

Subtract $5 x$ from both sides of the inequality.

$y \geq 3 x - 2 - 5 x$

Subtract $5 x$ from $3 x$ .

$y \geq - 2 x - 2$

Step 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 $y = m x + b$ .

$m = - 2$

$b = - 2$

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

Slope: $- 2$

y-intercept: $(0, - 2)$

Slope: $- 2$

y-intercept: $(0, - 2)$

Step 3

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

$y \geq - 2 x - 2$

Step 4