Question

The scatter graph shows some information about badge stalls at a festival.

Use the line of best fit to estimate the number of hours that a stall was open for
if it had 160 badges left to sell.
Number of badges left
Badge stalls and how long they were open for
300
200
100
6
Number of hours open
10
12

Answer 1

The stall was open for 5 hours .

From the graph given, we can use the pair of points to obtain the equation of best fit in the form : y = bx + c

• b = slope ; c = intercept
• (4, 180) ; (8, 100)

slope, b = (100-180)/(8-4) = -20

y = -20x + c

• (8, 100)

100 = -20(8) + c

100 = -160 + c

c = 260

Now we have :

y = -20x + 260

b.)

y = 160

160 = -20x + 260

160 - 260 = -20x

-100 = -20x

x = 5

Hence, the stall was open for 5 hours .