Question

question 1-3
the table shows a linear function. what is the rate of change?

x	1	1.5	2	2.5	3
y	18	23	28	33	38

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) of a linear function is given by $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in $y$ and $\Delta x$ is the change in $x$.

Step2: Choose two points

Let's take the first two points: $(x_1, y_1) = (1, 18)$ and $(x_2, y_2) = (1.5, 23)$.

Step3: Calculate $\Delta y$ and $\Delta x$

$\Delta y = y_2 - y_1 = 23 - 18 = 5$
$\Delta x = x_2 - x_1 = 1.5 - 1 = 0.5$

Step4: Compute rate of change

Rate of change $= \frac{\Delta y}{\Delta x} = \frac{5}{0.5} = 10$
We can verify with another pair, e.g., $(2, 28)$ and $(2.5, 33)$: $\Delta y = 33 - 28 = 5$, $\Delta x = 2.5 - 2 = 0.5$, so $\frac{5}{0.5} = 10$.

Answer:

10