Queston 12 The coffee shop lava Jive hasprices that increase linearly based on the size of the coffee, A 16 ounce coffee cosis 43.35 , and a 20 -0unce coffee cosis 43.75 . Let \( \% \) represent the cost, in dollars, of an in ounce coffee. White the equation representing this situation in point slope form. Then write the equation in slope intercept form. (Please use decimala instead of fractions in your answers.) point-slope form \( \square \) slope intercept forms \( \square \) Question Helpi Q Message inscrictor Submil Question

To model the relationship between the size of the coffee (in ounces) and its cost (in dollars) at Lava Jive, we'll use a linear equation. Let's define: - Let \( C \) represent the cost, in dollars, of an ounce of coffee. - \( x \) represents the size of the coffee in ounces. Given the two data points: - \( (16, 43.35) \) - \( (20, 43.75) \) ### 1. **Calculate the Slope (\( m \))** The slope \( m \) of the linear equation can be determined using the formula: \[ m = \frac{C_2 - C_1}{x_2 - x_1} \] Plugging in the values: \[ m = \frac{43.75 - 43.35}{20 - 16} = \frac{0.40}{4} = 0.10 \] ### 2. **Point-Slope Form** The point-slope form of a linear equation is: \[ C - C_1 = m (x - x_1) \] Using the point \( (16, 43.35) \): \[ C - 43.35 = 0.10 (x - 16) \] **Point-Slope Form:** \[ C - 43.35 = 0.10(x - 16) \] ### 3. **Slope-Intercept Form** The slope-intercept form is: \[ C = mx + b \] To find \( b \), use one of the points. Using \( (16, 43.35) \): \[ 43.35 = 0.10 \times 16 + b \\ 43.35 = 1.60 + b \\ b = 43.35 - 1.60 \\ b = 41.75 \] **Slope-Intercept Form:** \[ C = 0.10x + 41.75 \] ### **Final Answers** - **Point-Slope Form:** \[ C - 43.35 = 0.10(x - 16) \] - **Slope-Intercept Form:** \[ C = 0.10x + 41.75 \]