lines and slope intercept

Question

In 2008, an oak tree was planted by the parking lot at Secondary School In 2008, the tree was just 6 feet tall. When the tree was measured again in 2020, it was 24 feet tall. When the tree is 50 feet tall what year is it?

You need to find the slope and y intercept first y=mx=b

Answer 1

y = mt + b, where t is time in years from 2008 and y is height of tree. So we have 2 points: (0, 6) and (12, 24);

in 2020 t = 2020 - 2008 = 12, in 2008 t = 0.

Slope m = (24 - 6)/((12 - 0) = 1.5 feet per year. So y = 1.5·0 + b = 8, b = 8 feet and y = 1.5t + 8

If y = 50 then 50 = 1.5t + 8; t = 42/1.5 = 28 years.

So, in 2008 + 28 = 2036 year tree will be 50 feet tall.