Mathematics
Grade-8
Easy
Question
In the scatterplot shown below, a line has been drawn to show the trend in a population of box turtles over a period of twelve months.
Estimate the population of box turtles after 15 months.
- 440 turtles
- 40 turtles
- 149 turtles
- 90 turtles
Hint:
Find the slope intercept form of linear equation with given points and substitute the value.
The correct answer is: 149 turtles
The given points are (x1, y1) = (0,29) and (x₂, y₂) = (7, 85).
Step 1: Find the slope of the function using the slope formula:
m = (y₂ - y1) / (x₂ - x1) = (85 - 29) / (7 - 0) = 56/7 = 8.
Step 2: Find the equation of linear function using the point slope form.
y - y1 = m (x - x1)
y - 29 = 8 (x - 0)
y - 29 = 8 (x)
y = 8(x) + 29
To find the population of box turtles after 15 months substitute the value of x as 15 in the above equation
y = 8(15) + 29
y = 149
Thus, the population of box turtles after 15 months is 149.
Therefore, the equation of the linear function is, y = -1/2(x) + 6.
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