Graph 3x-2y<10

$3 x - 2 y < 10$

Step 1

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

Solve for $y$ .

Subtract $3 x$ from both sides of the inequality.

$- 2 y < 10 - 3 x$

Divide each term in $- 2 y < 10 - 3 x$ by $- 2$ and simplify.

Divide each term in $- 2 y < 10 - 3 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{10}{- 2} + \frac{- 3 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} > \frac{10}{- 2} + \frac{- 3 x}{- 2}$

Divide $y$ by $1$ .

$y > \frac{10}{- 2} + \frac{- 3 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

Step 2

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

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

$m = \frac{3}{2}$

$b = - 5$

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

Slope: $\frac{3}{2}$

y-intercept: $(0, - 5)$

Slope: $\frac{3}{2}$

y-intercept: $(0, - 5)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{3}{2} x - 5$ .

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

Step 4

Graph 3x-2y<10

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