Graph -x+2y-4<0

$- x + 2 y - 4 < 0$

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

Solve for $y$ .

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

Add $x$ to both sides of the inequality.

$2 y - 4 < x$

Add $4$ to both sides of the inequality.

$2 y < x + 4$

Divide each term in $2 y < x + 4$ by $2$ and simplify.

Divide each term in $2 y < x + 4$ by $2$ .

$\frac{2 y}{2} < \frac{x}{2} + \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} < \frac{x}{2} + \frac{4}{2}$

Divide $y$ by $1$ .

$y < \frac{x}{2} + \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$y < \frac{x}{2} + 2$

Reorder terms.

$y < \frac{1}{2} x + 2$

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 dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{2} x + 2$ .

$y < \frac{1}{2} x + 2$