Algebra Examples

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

Step 1

Graph $y \leq x$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.1.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 1$

$b = 0$

Step 1.1.3

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: $(0, 0)$

Step 1.2

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x$ .

$y \leq x$

Step 2

Graph $5$ .

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.1.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 0$

$b = 5$

Step 2.1.3

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

Slope: $0$

y-intercept: $(0, 5)$

Slope: $0$

y-intercept: $(0, 5)$

Step 2.2

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 5 \end{array}$

Step 2.3

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

Slope: $0$

y-intercept: $(0, 5)$

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 5 \end{array}$

Slope: $0$

y-intercept: $(0, 5)$

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 5 \end{array}$

Step 3

Graph $y \leq 2 x + 3$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 3.1.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 2$

$b = 3$

Step 3.1.3

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

Slope: $2$

y-intercept: $(0, 3)$

Slope: $2$

y-intercept: $(0, 3)$

Step 3.2

Graph a solid line, then shade the area below the boundary line since $y$ is less than $2 x + 3$ .

$y \leq 2 x + 3$

Step 4

Plot each graph on the same coordinate system.

$y \leq x$

$5$

$y \leq 2 x + 3$

Step 5