Question

a machine is filling a container with candy. the graph below shows the relationship between the amount of candy c (in grams) in the container and the tim (in seconds) since the machine began filling the container.
(a) write an equation to represent the relationship between c and t.

Explanation:

Step1: Identify slope formula

The relationship is linear, so use slope formula $m=\frac{C_2-C_1}{T_2-T_1}$. Pick points $(0,0)$ and $(10,1000)$.

Step2: Calculate the slope

$$\begin{align*} m&=\frac{1000-0}{10-0}\\ &=100 \end{align*}$$

Step3: Find y-intercept

When $T=0$, $C=0$, so intercept $b=0$.

Step4: Write linear equation

Use $C=mT+b$, substitute $m=100$, $b=0$.
$C=100T$

Answer:

$C=100T$