Algebra Examples

$5 x - 7 y > - 14$ $x \leq 7$

Step 1

Graph $5 x - 7 y > - 14$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Solve for $y$ .

Tap for more steps...

Step 1.1.1.1

Subtract $5 x$ from both sides of the inequality.

$- 7 y > - 14 - 5 x$

Step 1.1.1.2

Divide each term in $- 7 y > - 14 - 5 x$ by $- 7$ and simplify.

Tap for more steps...

Step 1.1.1.2.1

Divide each term in $- 7 y > - 14 - 5 x$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 y}{- 7} < \frac{- 14}{- 7} + \frac{- 5 x}{- 7}$

Step 1.1.1.2.2

Simplify the left side.

Tap for more steps...

Step 1.1.1.2.2.1

Cancel the common factor of $- 7$ .

Tap for more steps...

Step 1.1.1.2.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} < \frac{- 14}{- 7} + \frac{- 5 x}{- 7}$

Step 1.1.1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{- 14}{- 7} + \frac{- 5 x}{- 7}$

Step 1.1.1.2.3

Simplify the right side.

Tap for more steps...

Step 1.1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.1.1.2.3.1.1

Divide $- 14$ by $- 7$ .

$y < 2 + \frac{- 5 x}{- 7}$

Step 1.1.1.2.3.1.2

Dividing two negative values results in a positive value.

$y < 2 + \frac{5 x}{7}$

Step 1.1.2

Rearrange terms.

$y < \frac{5 x}{7} + 2$

Step 1.1.3

Reorder terms.

$y < \frac{5}{7} x + 2$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$m = \frac{5}{7}$

$b = 2$

Step 1.2.2

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

Slope: $\frac{5}{7}$

y-intercept: $(0, 2)$

Slope: $\frac{5}{7}$

y-intercept: $(0, 2)$

Step 1.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{5}{7} x + 2$ .

$y < \frac{5}{7} x + 2$

Step 2

Graph $x \leq 7$ .

$x \leq 7$

Step 3

Plot each graph on the same coordinate system.

$5 x - 7 y > - 14$

$x \leq 7$

Step 4