Write an equation in point-slope form to represent each situation. Assume a linear relationship between the given quantities.
A temperature of 50 degrees Fahrenheit corresponds to 10 degrees Celcius. A temperature of 77degrees Fahrenheit corresponds to 25 degrees Celsius. Write an equation giving Celsius temperature in terms of Fehrenheit temperature.
C = (F-32)5/9
To write the equation in point-slope form, we need to use the given information to find the slope and a point on the line.
First, let's find the slope. We can use the formula: slope = (change in y) / (change in x).
The change in Celsius temperature is 25 - 10 = 15 degrees.
The change in Fahrenheit temperature is 77 - 50 = 27 degrees.
So the slope is 15/27, or 5/9.
Next, let's find a point on the line. We can use the information given:
(50, 10) is a point on the line.
Now we can write the equation using the point-slope form:
y - y1 = m(x - x1)
Let's use the point (50, 10):
y - 10 = (5/9)(x - 50)
Simplifying this equation gives the final answer:
y - 10 = (5/9)(x - 50)
To write an equation in point-slope form, we need to determine the slope and use one of the given points.
Let's start by finding the slope. The slope represents how the Celsius temperature changes with respect to the Fahrenheit temperature. In other words, the slope represents the rate of change.
To find the slope, we use the formula: slope = (change in y)/(change in x). In this case, the y-value is the Celsius temperature, and the x-value is the Fahrenheit temperature.
Let's choose the two given points: (50, 10) and (77, 25).
The change in y is: 25 - 10 = 15.
The change in x is: 77 - 50 = 27.
So, the slope is: slope = 15/27.
Now that we have the slope, we can write the equation in point-slope form using either of the given points. Let's use the first point (50, 10).
The point-slope form of an equation is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
Plugging in the values, we have:
Celsius temperature (y) - 10 = (15/27) * (Fahrenheit temperature (x) - 50).
Therefore, the equation in point-slope form that represents the situation is:
Celsius temperature - 10 = (15/27) * (Fahrenheit temperature - 50).