Question

Billy's plant grows at least 2 inches a month.

Answer 1

Answer:

$y=2x+k$

Step-by-step explanation:

$y=2x+k$

Here we are given that the plant growth is fixed by 2 inches for every month.

hence ,

if we assume that the plant had zero height at beginning , when the time was also zero, then in the next month that is 1st month the height of the plant will be 2 inches, similarly in the 2nd month the height will be 4 inches , for the third month the height of the plant will be 6 inches and so on.

So, if we plot them on a graph , taking time in month on x axis and height of the plant on y axis , the pattern of growth as mentioned above will give us few coordinates like,

(0,0) , (1,2) , (2,4) , (3,6) and so on..

hence from here we can determine equation which refers the above situation by using two point form of an equation . The two point form is given as

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

where

$(x_1,y_1)$ and $(x_2,y_2)$ are $(1,2)$ and $(2,4)$ respectively

substituting them in the above formula we get

$\frac{y-2}{x-1}=\frac{4-2}{2-1}$

$\frac{y-2}{x-1}=2$

$y-2=2(x-1)$

$y-2=2x-2$

$y=2x$

Hence we get out scenario , in equation as $y=2x$

Note:

this is the situation when the height of the plant was considered 0 at time 0 . however , if the initial height of the plant was k ( assumption )

The equation would have been like this

$y=2x+k$

This is because in both the cases the slope of the line would be same , as slope represents the rate of increase of y with respect to x . in this case it would be the increased in the height of the plant with respect to the months Where k represent the value of y at x= 0 , or the height of the plant at time 0 month.

Please refer to the image attached with this.

Answer 2

We can assume that this growth rate can be expressed as y = mx + b as long as the slope is constant, because a quadratic or exponential formula wouldn't make much sense in this situation. If it is growing at least 2 inches a month, the slope (m) will be 2. As x (month) increases by 1 month, y (plant's height) increases by 2 inches. You could make it more, but as long as you plot the points in such a way that the slope for these points are 2 or higher, you will get the answer correct. If you have any other questions or need to clarify more about what you wanted let me know and I'll help.