Question

modeling real life a one-year-old boa constrictor is 26 inches long and grows 8 inches per year. write an equation in slope-intercept form that represents the length y (in feet) of a boa constrictor that is x years old.

Explanation:

Step1: Identify slope and intercept

The slope-intercept form is \( y = mx + b \), where \( m \) is the slope (rate of growth) and \( b \) is the y-intercept (initial length). The boa grows 8 inches per year, so \( m = 8 \). The initial length (when \( x = 0 \), a 0-year-old boa? Wait, no, the one-year-old is 26 inches. Wait, maybe recheck: Wait, the problem says "a one-year-old boa constrictor is 26 inches long and grows 8 inches per year". Wait, maybe the initial length (when \( x = 1 \)) is 26? No, wait, slope-intercept: let's think again. Wait, maybe the age \( x \) is in years, starting from 0? Wait, no, the one-year-old is 26. Wait, maybe the problem is that at \( x = 1 \), \( y = 26 \), and the growth rate is 8 inches per year. Wait, no, maybe the initial length (when \( x = 0 \)) is \( 26 - 8 = 18 \)? Wait, no, that might be wrong. Wait, no, maybe the problem is that the boa is one-year-old (x=1) with length 26, and grows 8 inches per year. So the equation would be \( y - 26 = 8(x - 1) \), which simplifies to \( y = 8x + 18 \). Wait, let's check: when x=1, y=8(1)+18=26, which matches. So the slope \( m = 8 \), y-intercept \( b = 18 \). Wait, but maybe the problem is that the one-year-old is the starting point? Wait, no, slope-intercept form is \( y = mx + b \), where \( b \) is the value when \( x = 0 \). So if at \( x = 1 \), \( y = 26 \), and the rate is 8, then \( 26 = 8(1) + b \), so \( b = 18 \). Therefore, the equation is \( y = 8x + 18 \).

Step2: Write the equation

Using the slope-intercept form \( y = mx + b \), with \( m = 8 \) (growth rate) and \( b = 18 \) (initial length when \( x = 0 \), which would be a 0-year-old boa, length 18 inches, then at x=1, 18+8=26, which matches). So the equation is \( y = 8x + 18 \).

Answer:

\( y = 8x + 18 \)