The total length y is a linear function of the tail length x with great accuracy. The domain is the interval from 30mm to 200mm, and the range is the interval from 200mm to 1400 mm. The following two points are given: X0= 60mm, Y0= 455mm, X1=140mm, Y1= 1050mm. Find the equation of y as function of x. The answer (equation) is y=7.44x+9 but how do I get that???
Y=mx +b
yo=m*xo+b
455=60m+b
y=m*x1 + b
1050=m*140+b
You have two equations. Subtract the first from the second.
(1050-455)=m(140-60)+b(1-1)
solve for m,
then, put that m in either of the equations, and solve for b.
To find the equation of y as a function of x, you can use the two given points (X0, Y0) and (X1, Y1) and plug them into the general form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope, m:
m = (Y1 - Y0) / (X1 - X0)
= (1050mm - 455mm) / (140mm - 60mm)
= 595mm / 80mm
= 7.4375 (rounded to 4 decimal places)
The slope, m, is approximately 7.4375.
Now, we can find the y-intercept, b.
To do this, we select either one of the given points and substitute the values of x and y into the equation. Let's use the point (X0, Y0).
Y0 = m*X0 + b
455mm = 7.4375 * 60mm + b
455mm - (7.4375 * 60mm) = b
b = 9mm (rounded to the nearest whole number)
Hence, the y-intercept, b, is approximately 9.
Now, we have the slope (m) and the y-intercept (b), and we can substitute them into the equation y = mx + b:
y = 7.4375x + 9
Therefore, the equation of y as a function of x is y = 7.44x + 9 (rounded to 2 decimal places).
Let me know if you need any further clarification!