The equation that models the number of female eastern bluebirds observed, b, Â 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, Â 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, Â and t, the total number of eggs laid is t = 5b
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