Question

1. minutes, x 6 10 14 20 24 cars washed, y 3 5 7 10 12 equation:________________ estimate y when x = 15:________________ explaining the meaning in the context of the situation:

Explanation:

Step1: Find the slope

We use the formula for the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(6,3)$ and $(10,5)$. Then $m=\frac{5 - 3}{10 - 6}=\frac{2}{4}=0.5$.

Step2: Find the y - intercept

We use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Using the point $(6,3)$ and $m = 0.5$, we have $y-3=0.5(x - 6)$. Expanding gives $y-3=0.5x-3$, so $y = 0.5x$.

Step3: Estimate y when x = 15

Substitute $x = 15$ into the equation $y=0.5x$. So $y=0.5\times15 = 7.5$.

Answer:

Equation: $y = 0.5x$; Estimate y when $x = 15$: $7.5$; In the context of the situation, it means that if 15 minutes are spent, approximately 7.5 cars are washed. Since we can't wash half a car in reality, it could imply that on average, in 15 minutes, 7 or 8 cars are washed depending on the rounding convention and the actual washing process.