Graph ax+5y>3 y-2<2/5x

$a x + 5 y > 3$ $y - 2 < \frac{2}{5} x$

Graph $a x + 5 y > 3$ .

Find the slope and the y-intercept for the boundary line.

Rewrite in slope-intercept form.

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

$y = m x + b$

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

$5 y > 3 - a x$

Divide each term in $5 y > 3 - a x$ by $5$ and simplify.

Divide each term in $5 y > 3 - a x$ by $5$ .

$\frac{5 y}{5} > \frac{3}{5} + \frac{- a x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} > \frac{3}{5} + \frac{- a x}{5}$

Divide $y$ by $1$ .

$y > \frac{3}{5} + \frac{- a x}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y > \frac{3}{5} - \frac{a x}{5}$

Arrange the polynomial to follow the $y = m x + b$ form for slope and y-intercept.

$y = - \frac{a x}{5} + \frac{3}{5}$

Rewrite in slope-intercept form.

$y = - \frac{x}{5} a + \frac{3}{5}$

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

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

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

$b = \frac{3}{5}$

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: $(0, \frac{3}{5})$

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

y-intercept: $(0, \frac{3}{5})$

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

y-intercept: $(0, \frac{3}{5})$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $3$ .

$a x + 5 y > 3$

Graph $y - 2 < \frac{2}{5} x$ .

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

Solve for $y$ .

Simplify $\frac{2}{5} x$ .

Rewrite.

$y - 2 < 0 + 0 + \frac{2}{5} x$

Simplify by adding zeros.

$y - 2 < \frac{2}{5} x$

Combine $\frac{2}{5}$ and $x$ .

$y - 2 < \frac{2 x}{5}$

Add $2$ to both sides of the inequality.

$y < \frac{2 x}{5} + 2$

Reorder terms.

$y < \frac{2}{5} x + 2$

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

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

$m = \frac{2}{5}$

$b = 2$

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

Slope: $\frac{2}{5}$

y-intercept: $(0, 2)$

Slope: $\frac{2}{5}$

y-intercept: $(0, 2)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{2}{5} x + 2$ .

$y < \frac{2}{5} x + 2$

Plot each graph on the same coordinate system.

$a x + 5 y > 3$

$y - 2 < \frac{2}{5} x$

Graph ax+5y>3 y-2<2/5x

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