write, in slope-intercept-form, the inequality shown in the graph. two points which the boundary line…
write, in slope-intercept-form, the inequality shown in the graph. two points which the boundary line intersects are shown.
Answer
Explanation:
Step1: Identify the coordinates of the two points
The boundary line passes through $(0, 8)$ and $(8, 0)$.
Step2: Calculate the slope of the boundary line
$$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{0 - 8}{8 - 0} = -1$$
Step3: Determine the y-intercept of the line
The line crosses the y-axis at $8$, so $b = 8$.
Step4: Write the equation of the boundary line
$$y = -x + 8$$
Step5: Determine the inequality symbol
The line is solid, and the shaded region is below the line. $$y \leq -x + 8$$
Answer:
$y \leq -x + 8$