Question

second is labeled 2, and so on. each step has the same height. the table below shows the step number and steps height from the base of the steps.
step number height from the base (meters)
50 10
90 18
110 22
write an equation to describe the relationship between n, the step number, and h, the height from the base.
equations may include exact decimals, proper fractions, or improper fractions.
please do not round or use mixed numbers.

Explanation:

Step1: Find slope (rate of change)

$\text{Slope} = \frac{h_2 - h_1}{n_2 - n_1} = \frac{18 - 10}{90 - 50} = \frac{8}{40} = \frac{1}{5}$

Step2: Verify slope with another pair

$\text{Slope} = \frac{22 - 18}{110 - 90} = \frac{4}{20} = \frac{1}{5}$

Step3: Find y-intercept (b)

Use $h = mn + b$, substitute $n=50, h=10$:
$10 = \frac{1}{5}(50) + b$
$10 = 10 + b$
$b = 0$

Step4: Write linear equation

Substitute $m=\frac{1}{5}, b=0$ into $h=mn+b$

Answer:

$h = \frac{1}{5}n$