Question

this graph shows the temperature of a room over time.
how many °f does the temperature of the room increase by every 1 min?
enter your answer in the box.
□ °f
temperature of a room
graph with temperature (°f) on y - axis from 10 to 80 and a line graph showing temperature over time

Explanation:

Step1: Identify coordinates

From the graph, initial point: (0, 65), final point: Let's assume time (x - axis) units. Let's see the grid. From 0 to, say, 5 minutes (assuming each grid is 1 min? Wait, no, let's check the temperature change. Wait, the temperature goes from 65 to 75. Let's count the time. Wait, maybe the time between 0 and 5 minutes? Wait, no, let's check the slope. Wait, the temperature increases from 65 to 75. Let's see the horizontal (time) and vertical (temperature) changes. Suppose at time t = 0, temp is 65. At t = 5, temp is 75? Wait, no, maybe the x - axis: each square is 1 minute? Wait, the graph: let's see the x - axis (time) and y - axis (temperature). Let's find two points. Let's say when time is 0 minutes, temperature is 65°F. When time is 5 minutes, temperature is 75°F? Wait, no, 75 - 65 = 10. So change in temperature (Δy) = 75 - 65 = 10°F. Change in time (Δx) = 5 minutes (assuming from 0 to 5 on x - axis). Then slope (rate) is Δy/Δx = 10/5 = 2? Wait, no, maybe I miscounted. Wait, let's look again. Wait, the first point is (0, 65), the second point: let's see the x - axis. Let's count the number of squares between 0 and the point where y = 75. If each x - grid is 1 minute, then from x = 0 to x = 5, y goes from 65 to 75. So Δy = 10, Δx = 5. So rate is 10/5 = 2? Wait, no, wait 75 - 65 = 10. If the time taken is 5 minutes, then per minute increase is 10/5 = 2? Wait, no, maybe the time is 5 minutes? Wait, maybe the x - axis: each unit is 1 minute. Wait, let's check the graph again. Wait, the temperature at x = 0 is 65, at x = 5 is 75. So the change in temperature is 75 - 65 = 10°F over 5 minutes. So per minute increase is 10/5 = 2? Wait, no, that can't be. Wait, maybe the x - axis is 5 minutes per grid? No, maybe I made a mistake. Wait, let's see: the temperature goes from 65 to 75. Let's count the vertical difference: 75 - 65 = 10. Horizontal difference: let's see the x - axis. If the horizontal (time) between 0 and the point where y = 75 is 5 units (minutes), then 10/5 = 2. Wait, but maybe the time is 5 minutes? Wait, no, maybe the x - axis is 1 minute per grid. Wait, maybe the two points are (0, 65) and (5, 75). So Δy = 10, Δx = 5. So rate is 10/5 = 2. Wait, no, 10 divided by 5 is 2? Wait, 10/5 = 2. So the temperature increases by 2°F per minute? Wait, no, wait 75 - 65 = 10. If the time is 5 minutes, then 10/5 = 2. So per minute, it's 2? Wait, no, maybe I messed up the time. Wait, maybe the x - axis is 1 minute per square. Let's see: from x = 0 to x = 5, that's 5 minutes. Temperature goes from 65 to 75, which is 10 degrees. So 10 degrees over 5 minutes is 2 degrees per minute. Wait, but let's check again. Wait, maybe the x - axis is 5 minutes? No, the problem says "every 1 min". So we need to find the rate of change (slope) of the line. The formula for slope (rate) is (y2 - y1)/(x2 - x1). Let's take two points: (0, 65) and (5, 75). Then (75 - 65)/(5 - 0) = 10/5 = 2. Wait, but maybe the x - axis is 5 minutes? No, the problem is about per 1 minute. So the rate is 2? Wait, no, wait 75 - 65 = 10. If the time between 0 and 5 is 5 minutes, then 10/5 = 2. So the temperature increases by 2°F every 1 minute? Wait, no, maybe I made a mistake. Wait, let's look at the graph again. Wait, the first point is (0, 65), the second point: let's see the x - axis. Let's count the number of units. If each x - unit is 1 minute, then from x = 0 to x = 5, y goes from 65 to 75. So Δy = 10, Δx = 5. So 10/5 = 2. So the rate is 2°F per minute. Wait, but maybe the x - axis is 1 minute, and the y - axis: 65 to 75 is 10, over 5 minutes? No, maybe the x - axis is 5 minutes? No, the problem is "every 1 min". So the correct calculation: find two points. Let's say at t = 0, T = 65. At t = 5, T = 75. Then rate = (75 - 65)/(5 - 0) = 10/5 = 2. So the temperature increases by 2°F every 1 minute. Wait, but maybe I miscounted the time. Wait, maybe the x - axis is 1 minute per grid, so from 0 to 5 is 5 minutes. So 10 degrees over 5 minutes is 2 degrees per minute. Yes, that makes sense.

Step2: Calculate rate

Rate of temperature increase = (Change in temperature) / (Change in time). Let ΔT = 75 - 65 = 10°F. Let Δt = 5 minutes (assuming the time between the two points is 5 minutes). Then rate = 10 / 5 = 2°F per minute. Wait, but maybe the time is 5 minutes? Wait, no, maybe the x - axis is 1 minute, and the two points are (0, 65) and (5, 75). So the rate is 2°F per minute.

Answer:

2