Graph x-y<1 x-7y>49

$x - y < 1$ $x - 7 y > 49$

Graph $x - y < 1$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- y < 1 - x$

Divide each term in $- y < 1 - x$ by $- 1$ and simplify.

Divide each term in $- y < 1 - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{1}{- 1} + \frac{- x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{1}{- 1} + \frac{- x}{- 1}$

Divide $y$ by $1$ .

$y > \frac{1}{- 1} + \frac{- x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

$y > - 1 + \frac{- x}{- 1}$

Dividing two negative values results in a positive value.

$y > - 1 + \frac{x}{1}$

Divide $x$ by $1$ .

$y > - 1 + x$

Rearrange terms.

$y > x - 1$

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 $y = m x + b$ .

$m = 1$

$b = - 1$

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

Slope: $1$

y-intercept: $(0, - 1)$

Slope: $1$

y-intercept: $(0, - 1)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $x - 1$ .

$y > x - 1$

Graph $x - 7 y > 49$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- 7 y > 49 - x$

Divide each term in $- 7 y > 49 - x$ by $- 7$ and simplify.

Divide each term in $- 7 y > 49 - x$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 y}{- 7} < \frac{49}{- 7} + \frac{- x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} < \frac{49}{- 7} + \frac{- x}{- 7}$

Divide $y$ by $1$ .

$y < \frac{49}{- 7} + \frac{- x}{- 7}$

Simplify the right side.

Simplify each term.

Divide $49$ by $- 7$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

$y < \frac{x}{7} - 7$

Reorder terms.

$y < \frac{1}{7} x - 7$

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

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

$m = \frac{1}{7}$

$b = - 7$

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

Slope: $\frac{1}{7}$

y-intercept: $(0, - 7)$

Slope: $\frac{1}{7}$

y-intercept: $(0, - 7)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{7} x - 7$ .

$y < \frac{1}{7} x - 7$

Plot each graph on the same coordinate system.

$x - y < 1$

$x - 7 y > 49$

Graph x-y<1 x-7y>49

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