Answer:
B) Yes, because the slope is [tex]-\frac{25}{3}[/tex] and the zero is (12, 0)
Step-by-step explanation:
From inspection of the graph:
- y-intercept = (0, 100)
- Two points: (3, 75) and (6, 50)
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{50-75}{6-3}=-\dfrac{25}{3}[/tex]
Therefore, the equation of the line in slope-intercept form y = mx + b
(where m is the slope and b is the y-intercept) is:
[tex]y=-\dfrac{25}{3}x+100[/tex]
To find the zero (when y = 0), set the equation to zero and solve for x:
[tex]\implies -\dfrac{25}{3}x+100=0[/tex]
[tex]\implies \dfrac{25}{3}x=100[/tex]
[tex]\implies 25x=300[/tex]
[tex]\implies x=12[/tex]
Therefore, the zero is at (12, 0)
Therefore, the graph does represent the function because the slope is [tex]-\frac{25}{3}[/tex] and the zero is at (12, 0)
