Question

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

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

1. write an equation for the sequence containing the following ordered pairs. (3,5) and (5,9)

Explanation:

For Question 3:

Step1: Calculate slope (m)

Use points $(0,6)$ and $(2,7)$:
$m = \frac{7-6}{2-0} = \frac{1}{2}$

Step2: Identify y-intercept (b)

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

Step3: Write linear equation

Substitute $m$ and $b$ into $y=mx+b$:
$y = \frac{1}{2}x + 6$

Step1: Calculate slope (m)

Use points $(3,5)$ and $(5,9)$:
$m = \frac{9-5}{5-3} = \frac{4}{2} = 2$

Step2: Solve for y-intercept (b)

Substitute $m=2$, $x=3$, $y=5$ into $y=mx+b$:
$5 = 2(3) + b$
$5 = 6 + b$
$b = 5 - 6 = -1$

Step3: Write linear equation

Substitute $m$ and $b$ into $y=mx+b$:
$y = 2x - 1$

Answer:

$y = \frac{1}{2}x + 6$

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For Question 4: