Let's assume that we want to write a linear equation representing the number of cookies y left after x days. If we decide to eat only 2 cookies each day, the number of cookies will decrease at a constant rate. This means that the slope of the equation will be - 2.
m= - 2
Now, let's assume that we know that at the beginning we had 26 cookies. Since the initial number of cookies represents the y-intercept, we would rather use slope-intercept form.
y= - 2x+ 26
However, let's assume that we have no information about the initial number of cookies but instead we know that after 3 days we have 20 cookies left. Therefore, the point ( 3, 20) satisfies the equation and we should choose point-slope form.
y- 20= - 2(x- 3)
We can see that depending on the type of information we have, we can choose different forms to represent the equation.
