Question

1. write an equation for the sequence represented by the following table.

x | 0 | 2 | 4 | 5
y | 6 | 7 | 8 | 8.5

Explanation:

Step1: Identify slope (rate of change)

Take two points, e.g., $(0,6)$ and $(2,7)$. Calculate slope:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-6}{2-0}=\frac{1}{2}=0.5$$

Step2: Find y-intercept

When $x=0$, $y=6$, so $b=6$.

Step3: Write linear equation

Use slope-intercept form $y=mx+b$.
$$y=0.5x+6$$
Verify with other points:
For $x=4$: $y=0.5(4)+6=8$ (matches table)
For $x=5$: $y=0.5(5)+6=8.5$ (matches table)

Answer:

$y=\frac{1}{2}x+6$ (or $y=0.5x+6$)