Question

solve the system of two linear inequalities graphically. \

$$\begin{cases} 8y - 8x > 32 \\\\ y > 1 \\end{cases}$$

step 1 of 3 : graph the solution set of the first linear inequality.

Explanation:

Step1: Rewrite inequality in slope-intercept form

Start with the first inequality:
$8y - 8x > 32$
Add $8x$ to both sides:
$8y > 8x + 32$
Divide all terms by 8:
$y > x + 4$

Step2: Identify boundary line

The boundary line is the equality $y = x + 4$. Since the inequality uses $>$, the line will be dashed (not included in the solution set).

Step3: Determine shaded region

Choose a test point not on the line, e.g., $(0,0)$:
Substitute into $y > x + 4$:
$0 > 0 + 4$ which is $0 > 4$, a false statement.
So we shade the region opposite to where $(0,0)$ lies, i.e., above the dashed line $y = x + 4$.

Answer:

Graph a dashed line with slope $1$ and y-intercept $(0,4)$, then shade the region above this line.