Question

this question has two parts. first, answer part a. then, answer part b.
growth suppose the body length y in inches of a baby snake is given by 4x - 2y = -3, where x is the age of the snake in months until it becomes 1 year old.
part a
a. write the equation in slope - intercept form.
part b
b. interpret the parameters of the equation in the context of the situation.
when the snake hatched, it was

inches long. it grows at a rate of

inches each month for the first

months

Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We start with the equation $4x-2y=-3$.
First, we want to isolate $y$ on one side of the equation. Subtract $4x$ from both sides:
$-2y=-4x - 3$
Then, divide each term by $-2$:
$y=\frac{-4x}{-2}+\frac{-3}{-2}$
Simplify the fractions:
$y = 2x+\frac{3}{2}$

Step2: Interpret the parameters (Part B)

The slope - intercept form of the equation is $y=mx + b$, where $m$ is the rate of change (slope) and $b$ is the initial value (y - intercept).

• When the snake hatched, $x = 0$ (age is 0 months). Substitute $x = 0$ into the equation $y=2x+\frac{3}{2}$. Then $y=\frac{3}{2}=1.5$. So when the snake hatched, it was $1.5$ inches long.
• The slope $m = 2$. In the context of the problem, since $y$ is the body length and $x$ is the age in months, the slope represents the rate of growth. So it grows at a rate of $2$ inches per month.
• The domain of $x$ (age in months) for the first growth period is from $x = 0$ (hatching) until it becomes 1 year old. Since 1 year is 12 months, the time period is 12 months. But from the equation's context, we are looking at the first 12 months (until it is 1 year old). However, from the equation $y = 2x+\frac{3}{2}$, the "first" period here is likely until it is 1 year old, so the number of months is 12. But let's focus on the first two blanks first. The y - intercept is $\frac{3}{2}$ (or 1.5) which is the length at hatching, and the slope is 2 which is the growth rate per month.

Answer:

(Part A):
The equation in slope - intercept form is $y = 2x+\frac{3}{2}$