Final answer:
To find the relationship between Celsius and Fahrenheit, calculate the slope (1.8) using two points and derive the linear equation: y = (9/5)x + 32. The graph is a straight line with a y-intercept of 32.
Step-by-step explanation:
The relationship between the Fahrenheit and Celsius temperature scales can be modeled with a linear graph, where the Celsius temperature is represented on the x-axis and the Fahrenheit temperature is represented on the y-axis. Given two points, Temp. A (50°C, 122°F) and Temp. B (100°C, 212°F), we can calculate the slope (m) of the line that models the relationship between the two scales.
First, we calculate the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Applying this formula, we get m = (212 - 122) / (100 - 50) = 90 / 50 = 9/5, which is the ratio of Fahrenheit degrees to Celsius degrees, and is a constant of 1.8.
Next, we find the y-intercept (b) of the line. By knowing that the freezing point of water is 0°C and corresponds to 32°F, we can use one of the points and the slope to solve for b in the equation y = mx + b. So we use the freezing point: 32 = (9/5)(0) + b, which means b = 32.
The final linear equation in slope-intercept form that represents the relationship between Fahrenheit and Celsius is y = (9/5)x + 32. Graphically, this line will cross the y-axis at 32 (the value of b) and will increase by 1.8 degrees Fahrenheit for every increase of 1 degree Celsius.