Answer:
The inequality that represents the graph is y < [tex]\frac{1}{4}[/tex]x + 2
Step-by-step explanation:
i) the region below a dashed line through the points (4,3) and (0,2) is shaded.
ii) first we find the equation of the line passing through the points (4,3) and (0,2)
(y - 3) = [tex](\frac{3 - 2}{4 - 0})[/tex](x - 4) ⇒ y - 3 = [tex]\frac{1}{4}[/tex](x - 4)
⇒ 4y - 12 = x - 4 ⇒ 4y = x + 8 ⇒ y = [tex]\frac{1}{4}[/tex]x + 2
iii) for the area shaded below the line whose equation is given in ii) above the inequality that will represent the shaded region is given by
y < [tex]\frac{1}{4}[/tex]x + 2
