Question

At 9:00 AM, the temperature started rising 2°F per hour until it reached 24°F at 2:00 PM. What was the temperature at 9:00 AM?

Answer 1

Explanation:

I'm assuming that you are studying linear algebra right now. If not, that's how I'm solving this, so bear with me.

Let's start by saying that 9 am is time 0. That means that

10 am is time 1

11 am is time 2

noon is time 3

1 pm is time 4

2 pm is time 5

Those times are the x values. The only one we really need to worry about is the one given to us: time 5, temp 24. The temp is the y value, so the resulting coordinate is (5, 24). We already know that the temp is steadily increasing 2 degrees per hour, so 2 is the slope of the line modeling this situation. Using that info in the point-slope form of a line:

y - 24 = 2(x - 5) and

y - 24 = 2x - 10 and

y = 2x + 12

If 9 am is time 0, sub in a 0 for x and solve for y, the temp at 9 am:

y = 2(0) + 12 so

y = 12 degrees at 9 am.