Caroline knows that the more educational workshops she hosts at the giraffe exhibit, the more donations people make to the giraffes, which helps fund their care. However, she's worried because when the female giraffe gives birth, they'll have to stop doing the educational workshops for a few weeks to let the baby giraffe acclimate.

Question

Last week, Caroline held 12 educational workshops and the giraffes received $1,643 of donations. This week, she held 9 educational workshops and the giraffes received $1,364 of donations.
Which linear equation represents the scenario in #1?

y=93x+527

y=12x+1643

y=9x+1364

y=83x

Answer 1

To find the linear equation that represents the relationship between the number of educational workshops \( x \) and the donations received \( y \), we can analyze the provided data points.

1. From last week:

   • Number of workshops \( x = 12 \)
   • Donations \( y = 1643 \)

2. From this week:

   • Number of workshops \( x = 9 \)
   • Donations \( y = 1364 \)

We can calculate the slope \( m \) of the linear relationship using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) \) is the first point \((12, 1643)\) and \( (x_2, y_2) \) is the second point \((9, 1364)\).

Calculating the slope: \[ m = \frac{1364 - 1643}{9 - 12} = \frac{-279}{-3} = 93 \]

Now, we know the slope is 93. We can use the point-slope form of the linear equation, \( y - y_1 = m(x - x_1) \), to find the equation.

Using point \( (12, 1643) \): \[ y - 1643 = 93(x - 12) \] Expanding this: \[ y - 1643 = 93x - 1116 \] Adding \( 1643 \) to both sides: \[ y = 93x + 527 \]

Thus, the linear equation that represents the scenario is: \[ y = 93x + 527 \]

Therefore, the answer is: y = 93x + 527