Graph 2x-7y<=14

$2 x - 7 y \leq 14$

Step 1

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

Solve for $y$ .

Subtract $2 x$ from both sides of the inequality.

$- 7 y \leq 14 - 2 x$

Divide each term in $- 7 y \leq 14 - 2 x$ by $- 7$ and simplify.

Divide each term in $- 7 y \leq 14 - 2 x$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 y}{- 7} \geq \frac{14}{- 7} + \frac{- 2 x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} \geq \frac{14}{- 7} + \frac{- 2 x}{- 7}$

Divide $y$ by $1$ .

$y \geq \frac{14}{- 7} + \frac{- 2 x}{- 7}$

Simplify the right side.

Simplify each term.

Divide $14$ by $- 7$ .

$y \geq - 2 + \frac{- 2 x}{- 7}$

Dividing two negative values results in a positive value.

$y \geq - 2 + \frac{2 x}{7}$

Rearrange terms.

$y \geq \frac{2 x}{7} - 2$

Reorder terms.

$y \geq \frac{2}{7} x - 2$

Step 2

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

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

$m = \frac{2}{7}$

$b = - 2$

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

Slope: $\frac{2}{7}$

y-intercept: $(0, - 2)$

Slope: $\frac{2}{7}$

y-intercept: $(0, - 2)$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{2}{7} x - 2$ .

$y \geq \frac{2}{7} x - 2$

Step 4

Graph 2x-7y<=14

Related Questions

Support LCMGCF.com by disabling your adblocker.