write the function in slope-intercept form (in description)

Question

A bonsai plant is 5 cm tall and growing at a rate of 3 cm a year. Write the function H(y), in slope-intercept form, that models the bonsai's height.

Answer 1

Slope-intercept form is y = mx + b, where m is the slope and y is the y-intercept.

In this case, our variables are Height in cm and time in years. We're asked to write an equation for Height in terms of time H(y), So we know to start with H(y) = and fill in the rest.

The slope comes from the rate in the problem. A rate is something that indicates division...in this equation it's the units "cm a year." This corresponds to the units cm/y, which are divided and tell us how fast (the rate) that the plant is growing: 3 cm/year. This is the m value.

The y-intercept is the starting point of the graph. In other words, what is the height of the plant when zero years have passed? In the problem, we're given that the bonsai plant is 5 cm tall at the beginning. So 5 cm is our b value.

When we plug it into the equation, we get:

H(y) = m*y + b

H(y) = 3*y + 5

Adding in the units...

H(y) = (3 cm/year) * y + 5 cm

We can see that indeed, the height is zero when y (the number of years) is zero. Also, for every year y, we multiply by 3 because it's growing by 3 cm/year.

Answer 2

H(y) = 3y + 5