GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A meteorologist is tracking the temperature change in a city. At 8 AM, the temperature was 50°F. By 1 PM, the temperature had risen to 65°F. Assuming a constant rate of change, which equation models the temperature, T, in degrees Fahrenheit, as a function of the time, h, in hours, since 8 AM?
- AT = 3h + 50
- BT = 5h + 50
- CT = 3h + 65
- DT = 15h + 50
Show answer & explanationAnswer & explanation
Correct answer: A. T = 3h + 50
To find the equation, first calculate the slope (rate of change) using the given points. Then, use the point-slope form or slope-intercept form with the initial temperature as the y-intercept.
Why the other options are wrong
- B. This option uses an incorrect slope.
- C. This option uses the correct slope but an incorrect y-intercept (initial temperature).
- D. This option uses the total temperature change as the slope, not the rate per hour.
Linear Equation from Two Points
A linear equation can be determined from two given points by first calculating the slope, and then using one of the points and the slope to find the y-intercept.
- Slope (m) = (y2 - y1) / (x2 - x1)
- Equation form: y = mx + b
- Initial value often corresponds to the y-intercept (b).
Memory trick: Slope First, Then Intercept - that's the linear concept!