Question

A meteorologist tracks the amount of snowfall over a 5-hour period.She graphs her measurements. What is the equation of the meteorologist's linein slope-intercept form? Define your variables.Snowfall?

Answer 1

From the given graph, there are 2 points on it

(0, 3) and (2, 5)

∵ The form of the slope-intercept is y = m x + b, where

→ m is the slope of the line

→ b is the y-intercept (value y at x = 0)

∵ The rule of the slope is

`m=(y2-y1)/(x2-x1)`

Where (x1, y1) and (x2, y2) are two points on the line

∵ (0, 3) and (2, 5) lie on the line

∴ x1 = 0 and y1 = 3

∴ x2 = 2 and y2 = 5

→ Substitute them in the rule of the slope to find it

`\begin{gathered} \because m=(5-3)/(2-0) \\ \therefore m=(2)/(2)=1 \end{gathered}`

→ Substitute the value of m in the form of the equation above, but replace

y by f(h) and x by h

`\begin{gathered} \therefore f(h)=1(h)+b \\ \therefore f(h)=h+b \end{gathered}`

∵ b is the value of y at x = 0

∵ At x = 0, y = 3

∴ b = 3

→ Substitute the value of b in the equation above

`\therefore f(h)=h+3`

∴ The equation of the meteorologist's line is f(h) = h + 3, where

f(h) is the amount of snow and h, is the time