The equation that models the number of female eastern bluebirds observed, b, and t, the total number of eggs laid is t = 5b
If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
y = mx +c
To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.
Let we take:
b = the number of female eastern bluebirds observed
t = the total number of eggs laid
Since the relationship between b and t is forming a line, so it can be modeled by linear equation.
Here, we take 'b' as independent variable, and the value of 't' depending on the value of 'b', and therefore, let the linear equation representing them is:
[tex]t = mb + c[/tex]
For this case, we see that as the number of female eastern bluebird is increased by 1, half of 10 units (which is 5 units) is increased in the total number of eggs laid.
Thus, as we increase 'b' by 1 unit, there is increase by 5 units in the value of 't'.
and therefore, we get: m = increment in dependent variable per unit increment in independent variable = 5
Thus, the equation is:
[tex]t = 5b + c[/tex]
At b = 1, the number of eggs laid is 5, or t = 5, therefore, putting these values in the equation, we get:
[tex]5 = 5(1) = c\\c = 5-5=0[/tex]
Thus, the relation between t and b is t = 5b + 0= 5b
Thus, the equation that models the number of female eastern bluebirds observed, b, and t, the total number of eggs laid is t = 5b
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