the relationship between farenheit and celsius temp can be approximated by an equation of the form y=mx+b where x is degrees farenheit and y is degrees celsius. find the equation if the two ordered pairs that satify this equations are (50,10) and (86,30)
Your School Subject is Math.
GIVEN: ( 50,10 ) , ( 86,30 ).
Slope = (30-10) / (86-50) = 20/36 = 5/9. Y = mx + b, 10 = (5/9)(50) + b
Solve for b, b = 10 - (250/9) = 17.7777
EQUATION: Y = (5/9)X - 17.777
To find the equation of the relationship between Fahrenheit and Celsius temperatures, we can use the two given ordered pairs (50, 10) and (86, 30).
Let's assign Fahrenheit as x and Celsius as y. The equation relating the two will be in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Find the slope (m)
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two given points.
Substituting the values:
m = (30 - 10) / (86 - 50)
m = 20 / 36
m = 5/9
Step 2: Find the y-intercept (b)
To find b, we can substitute the values of one of the points into the equation y = mx + b and solve for b.
Using (50, 10):
10 = (5/9)(50) + b
10 = 250/9 + b
To simplify the equation, we can find a common denominator for the fractions by multiplying the denominator of 250/9 (which is 9) by the 50. This gives us:
10 = 1250/9 + b
We can now solve for b by subtracting 1250/9 from both sides of the equation:
10 - 1250/9 = b
90/9 - 1250/9 = b
-1160/9 = b
Therefore, b = -1160/9
Step 3: Write the equation using m and b
Now that we have the values of m and b, we can write the equation:
y = (5/9)x - 1160/9
So, the relationship between Fahrenheit (x) and Celsius (y) temperatures can be approximated by the equation y = (5/9)x - 1160/9.