Graph x+5y>=5 y<=2x+4

$x + 5 y \geq 5$ $y \leq 2 x + 4$

Step 1

Graph $x + 5 y \geq 5$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$5 y \geq 5 - x$

Divide each term in $5 y \geq 5 - x$ by $5$ and simplify.

Divide each term in $5 y \geq 5 - x$ by $5$ .

$\frac{5 y}{5} \geq \frac{5}{5} + \frac{- x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} \geq \frac{5}{5} + \frac{- x}{5}$

Divide $y$ by $1$ .

$y \geq \frac{5}{5} + \frac{- x}{5}$

Simplify the right side.

Simplify each term.

Divide $5$ by $5$ .

$y \geq 1 + \frac{- x}{5}$

Move the negative in front of the fraction.

$y \geq 1 - \frac{x}{5}$

Rearrange terms.

$y \geq - \frac{x}{5} + 1$

Reorder terms.

$y \geq - (\frac{1}{5} x) + 1$

Remove parentheses.

$y \geq - \frac{1}{5} x + 1$

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

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

$m = - \frac{1}{5}$

$b = 1$

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

Slope: $- \frac{1}{5}$

y-intercept: $(0, 1)$

Slope: $- \frac{1}{5}$

y-intercept: $(0, 1)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{5} x + 1$ .

$y \geq - \frac{1}{5} x + 1$

Step 2

Graph $y \leq 2 x + 4$ .

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 $y = m x + b$ .

$m = 2$

$b = 4$

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

Slope: $2$

y-intercept: $(0, 4)$

Slope: $2$

y-intercept: $(0, 4)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $2 x + 4$ .

$y \leq 2 x + 4$

Step 3

Plot each graph on the same coordinate system.

$x + 5 y \geq 5$

$y \leq 2 x + 4$

Step 4

Graph x+5y>=5 y<=2x+4

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