Algebra Examples

y \leq 3 + \frac{1}{2} x

$y \leq 3 + \frac{1}{2} x$

Step 1

Write in

y = m x + b

$y = m x + b$ form.

Tap for more steps...

Step 1.1

Simplify

3 + \frac{1}{2} x

$3 + \frac{1}{2} x$ .

Tap for more steps...

Step 1.1.1

Combine

\frac{1}{2}

$\frac{1}{2}$ and

x

$x$ .

y \leq 3 + \frac{x}{2}

$y \leq 3 + \frac{x}{2}$

Step 1.1.2

Reorder

3

$3$ and

\frac{x}{2}

$\frac{x}{2}$ .

y \leq \frac{x}{2} + 3

$y \leq \frac{x}{2} + 3$

y \leq \frac{x}{2} + 3

$y \leq \frac{x}{2} + 3$

Step 1.2

Reorder terms.

y \leq \frac{1}{2} x + 3

$y \leq \frac{1}{2} x + 3$

y \leq \frac{1}{2} x + 3

$y \leq \frac{1}{2} x + 3$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Step 2.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = \frac{1}{2}

$m = \frac{1}{2}$

b = 3

$b = 3$

Step 2.2

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

\frac{1}{2}

$\frac{1}{2}$

y-intercept:

(0, 3)

$(0, 3)$

Slope:

\frac{1}{2}

$\frac{1}{2}$

y-intercept:

(0, 3)

$(0, 3)$

Step 3

Graph a solid line, then shade the area below the boundary line since

y

$y$ is less than

\frac{1}{2} x + 3

$\frac{1}{2} x + 3$ .

y \leq \frac{1}{2} x + 3

$y \leq \frac{1}{2} x + 3$

Step 4