I need to solve this problem....

[zaheer_abbas]

the length of a steel beam is a linear function of the temperature. When temperatures is 40F a certain steel beam is 50 fit long and at 95F the same beam is 50.12 feet long. what is the length of the beam at 70F? At what temperatures is the beam 49.9 feet long?

 

[stapel]

the length of a steel beam is a linear function of the temperature.

So the length (let's call it "L") is a function of (stands in for "y") of the temperature (let's call it "T"). And it's a "linear" function, so you need a straight-line equation (like they explain here, just with "L = mT + b" instead of "y = mx + b").

When temperatures is 40F a certain steel beam is 50 fit long and at 95F the same beam is 50.12 feet long. what is the length of the beam at 70F?

You are given two points, the first being (T, L) = (40, 50). Use those points to find the slope of the line through the points (link). Then use that slope and either of the points (it doesn't matter which) to find the straight-line equation. This is your "model".

At what temperatures is the beam 49.9 feet long?

Plug the specified length value into your model, and solve for the corresponding temperature.

If you get stuck, please reply showing all of your steps so far. Thank you!