Question

text to speech
calcu
graph the inequality.
$y > x + 12$
a)

Explanation:

Step1: Identify boundary line

The boundary of $y > x + 12$ is the line $y = x + 12$, which has a slope of $1$ and y-intercept at $(0,12)$. Since the inequality is $>$, the line is dashed (not included in the solution set).

Step2: Determine shaded region

Test a point not on the line, e.g., $(0,0)$:
$0 > 0 + 12$ simplifies to $0 > 12$, which is false. So we shade the region above the line (where points satisfy $y > x + 12$).

Step3: Match to option A

Option A shows a dashed line with slope 1, and shading above the line, which matches the requirements for $y > x + 12$.

Answer:

A) [The graph with a dashed line $y=x+12$ and shading above the line]