Question

allie orders candies from an online company that offers flat rate shipping. she placed an order for 4 candles for $35. a few months later, she placed an order for 12 candles for $95. a) write an equation to model the total cost, y, for ordering x candles. b) what does the slope & y - intercept mean in terms of the problem? c) how much is shipping?

Explanation:

Step1: Find the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(4,35)$ and $(x_2,y_2)=(12,95)$.
$m=\frac{95 - 35}{12 - 4}=\frac{60}{8} = 7.5$

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$. Substitute $m = 7.5$, $x_1 = 4$, $y_1 = 35$.
$y-35=7.5(x - 4)$
$y-35=7.5x-30$
$y=7.5x + 5$

Step3: Interpret the slope

The slope $m = 7.5$ means the cost per candle is $7.5$ dollars.

Step4: Interpret the y - intercept

The y - intercept $b = 5$ means the flat - rate shipping cost is $5$ dollars.

Answer:

a) The equation is $y = 7.5x+5$.
b) The slope ($7.5$) is the cost per candle. The y - intercept ($5$) is the flat - rate shipping cost.
c) The shipping cost is $\$5$.