Weather Station: Shared Readings

Use crossing graphs to identify readings that satisfy two linear equations.

Morning Temperature Models

Connect A to B and C to D with a ruler. These segments show two linear temperature models. Use the graph for Questions 1–4.

A weather station compares a courtyard model, y = x − 4, with a rooftop model, y = −x + 2. Here x is hours after 6 a.m., and y is temperature in °C. Use only times from x = 0 through x = 6.

Which ordered pair is the solution of this system?

A. (2, 0)B. (3, −1)C. (4, 0)D. (−1, 3)

The station flags the time when the two models predict the same temperature.

At what morning clock time should the flag appear? a.m.

The station issues a frost notice when both models predict the same temperature below 0°C. Which conclusion follows from the crossing?

A. A notice is due because both models predict −1°C at 9 a.m.B. A notice is due because both models predict 0°C at 8 a.m.C. No notice is due because the courtyard starts below 0°C.D. No notice is due because the rooftop starts above 0°C.

Which two equations verify the shared reading at the crossing? Select both.

Rainfall Record Checks

A table entry represents a point on a graph. A system solution must use the same x-value and the same y-value in both models.

During a storm, two rain gauges are modeled by y = 2x + 3 and y = 3x + 1. Here x is hours after noon, and y is total rainfall in millimeters.

Rain Gauge Models
Hours after noon	Gauge: 2x + 3	Gauge: 3x + 1
0	3	1
1	5	4
2	?	?
3	9	10

At x = 2, the first model predicts mm, and the second model predicts mm.

Use the rain gauge models from Question 5. Which graph description must be correct?

A. The lines cross at (2, 7).B. The lines cross at (0, 3).C. The lines cross at (3, 10).D. The lines cross at (7, 2).

A report says, “At 3 p.m., both rain gauges reach 10 mm, so (3, 10) is the system's solution.” Use the table in Question 5. Which correction is accurate?

A. At 3 p.m., both gauges predict 9 mm instead.B. At 3 p.m., the gauges predict 3 mm and 1 mm.C. At 3 p.m., the gauges predict 9 mm and 10 mm.D. At 3 p.m., the gauges predict 7 mm and 7 mm.

For another storm, the station graphs two rainfall models using x for hours after midnight and y for millimeters. Their only crossing is (5, 12). A report must include a time when both models predict at least 11 mm. Which entry meets that requirement?

A. At noon, both models predict 5 mm.B. At midnight, both models predict 12 mm.C. At 5 a.m., both models predict 5 mm.D. At 5 a.m., both models predict 12 mm.

A technician labels an intersection as (4, ?). The two rainfall equations are y = x + 5 and y = 2x + 1.

What y-coordinate makes (4, y) lie on both graphs?

Overnight Graph Review

For Questions 10–12, connect E to F and G to H. Negative x-values mean hours before midnight; positive x-values mean hours after midnight.

The station compares two overnight temperature models: y = x + 4 and y = −2x − 2. Temperature y is measured in °C.

10.

Read the crossing of the overnight temperature graphs.

The shared reading is (, ).

11.

Which station log entry correctly interprets the crossing in Question 10?

A. At 10 p.m., both models predict 2°C.B. At 2 a.m., both models predict 2°C.C. At 2 a.m., both models predict −2°C.D. At 10 p.m., both models predict −2°C.

12.

The overnight equations represent distinct lines. Why can there be no second shared reading on these two lines?

A. Two lines must have equal y-intercepts to cross.B. Two distinct lines can cross at most once.C. A line can contain only one negative x-value.D. A crossing prevents either line from reaching an axis.

13.

Luis reviews the morning models y = x − 4 and y = −x + 2. He says, “One graph reaches 0°C at x = 4, and the other reaches 0°C at x = 2. Since the zero readings happen at different times, the system has no solution.” Explain why his conclusion is incorrect. Include the actual shared ordered pair.