Complete the tables of values
1 answer:
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Answer:
The solutions are:
(-15 , -4) ⇒ 1st
(3 , 2) ⇒ 3rd
(21 , 8) ⇒ 5th
Step-by-step explanation:
To find the solution of the graph let us make the equation of the line by using any two points on the line
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
The formula of the slope is
From the figure
∵ The line passes through points (-3 , 0) and (0 , 1)
- Find the slope of the line
∴
- Substitute the value of m in the form of the equation
∴ y = x + b
∵ b is the value of y at x = 0
∵ y = 1 at x = 0 ⇒ y-intercept
∴ b = 1
∴ y = x + 1
Lets substitute the x-coordinate of each point to find the y-coordinate, if the y-coordinate is equal to the y-coordinate of the points, then the point is a solution
Point (-15 , -4)
∵ x = -15
∴ y = (-15) + 1
∴ y = -5 + 1 = -4 ⇒ same value of the point
∴ (-15 , -4) is a solution
Point (-6 , 1)
∵ x = -6
∴ y = (-6) + 1
∴ y = -2 + 1 = -1 ⇒ not the same value of the point
∴ (-6 , 1) is not a solution
Point (3 , 2)
∵ x = 3
∴ y = (3) + 1
∴ y = 1 + 1 = 2 ⇒ same value of the point
∴ (3 , 2) is a solution
Point (12 , 9)
∵ x = 12
∴ y = (12) + 1
∴ y = 4 + 1 = 5 ⇒ not the same value of the point
∴ (12 , 9) is not a solution
Point (21 , 8)
∵ x = 21
∴ y = (21) + 1
∴ y = 7 + 1 = 8 ⇒ same value of the point
∴ (21 , 8) is a solution
This problem can be solve by graphing (technology), as suggested.
The answer is posted as an attached image. We see that after about 14.75 years, the invading species will surpass the indigenous population.
If it needs to be solved mathematically and accurately, the math is a little more advanced, using the bisection method, or Newton's method.
However, we can also do that by trial and error, starting from 14.75. It is easier than you might think.
Post if you would like to have more information on one or the other methods.
Note: the scale of y has been shrunk by 1000, so each unit on the y-axis represents 1000 frogs.
The answer is posted as an attached image. We see that after about 14.75 years, the invading species will surpass the indigenous population.
If it needs to be solved mathematically and accurately, the math is a little more advanced, using the bisection method, or Newton's method.
However, we can also do that by trial and error, starting from 14.75. It is easier than you might think.
Post if you would like to have more information on one or the other methods.
Note: the scale of y has been shrunk by 1000, so each unit on the y-axis represents 1000 frogs.