Question

Cameron's grandparents gift him a puppy named Ruby for his thirteenth birthday. Cameron diligently cares for Ruby, witnessing her rapid growth. At 1 month, Ruby weighs 5 pounds, and at 2 months, she weighs 8 pounds.

Define the relationship with x as Ruby's age (in months) and y as her weight (in pounds).

Answer 1

The relationship between Ruby's age and weight can be represented by a linear function: y = 3x + 2.

Step-by-step explanation:

The relationship between Ruby's age (x) and her weight (y) can be represented by a linear function. In this case, we have two data points: at 1 month (x=1), Ruby weighs 5 pounds (y=5), and at 2 months (x=2), she weighs 8 pounds (y=8).

To find the equation of the line, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope of the line. Using the first data point (1, 5), we can substitute the values into the equation and solve for m:

y - 5 = m(x - 1)

8 - 5 = m(2 - 1)

3 = m

So the equation of the line is y - 5 = 3(x - 1) or y = 3x + 2.