Let y = f (x) be an implicit function determined by the functional equation ln (x + 2Y) = x ^ 2 + y ^ 2, and find y

Let y = f (x) be an implicit function determined by the functional equation ln (x + 2Y) = x ^ 2 + y ^ 2, and find y

F(x,y)=x^2+y^2-ln(x+2y) Fx=2x-1/(x+2y) Fy=2y-2/(x+2y)
F(x)=-Fx/Fy=-[2x(x+2y)-1]/[2y(x+2y)-2]

X ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 tangent equation at point (2a, √ 3b), normal equation PS: tangent slope is calculated by derivative, high number questions, don't use high school methods

2X / A ^ 2-2y * y '/ b ^ 2 = 0,
The solution is k = y '= (x / y) * (b ^ 2 / A ^ 2) = (2A / √ 3b) * (b ^ 2 / A ^ 2) = 2 √ 3B / (3a),
Therefore, the tangent equation is Y - √ 3B = 2 √ 3B / (3a) * (x-2a),
The normal equation is Y - √ 3B = - √ 3A / (2b) * (x-2a)

How to calculate the slope and y-intercept Please help me have a look 3 y=x+100 y=2x-5 y=o.5x How can I calculate the slope and intercept~

Where y = KX + B, K is the slope and B is the intercept on the Y axis
Y = x + 100, slope 1, intercept on Y axis 100
Y = 2x-5, slope 2, intercept on Y axis - 5
Y = o.5x, slope 0.5, intercept 0 on Y axis

What is a slope I study abroad, because it's English, I don't know how to translate. Maybe I haven't learned this at home. I hope to find someone who knows it well to help explain. It's best to give examples 1. Point slope I translate it in a dictionary. It seems to be the slope formula: Y-Y / x-x = M 2. Slope intercept formula is: y = MX + B

These are two ways to represent a straight line. The first is called the "point skew formula". The formula: Y-Y / x-x = the first y in M represents the dependent variable, the first X represents the independent variable, the second y and the second x represent the coordinates of any point through which the straight line passes, and M is the slope of the straight line, that is, when the slope of the straight line and the point it passes through are known

Is the slope of the linear regression equation the correlation coefficient? 6 questions  

The linear correlation coefficient is not the slope, but there is a connection between the two, which is reflected in the sign. The sign of positive correlation R is a positive sign, and the slope is also positive. Similarly, negative correlation is the same
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How is the slope of linear regression calculated

The linear equation is estimated by linear regression with the least square method
y=a+b*x;
The least square method obtains the estimated values a and B and substitutes them to obtain the estimated straight line}
Copy contents to clipboard code:
x: = k bar value;
y:=c;
b1:= Σ (x(i)-avr(x,30))*(y(i)-avr(y,30));
b2:= Σ (x(i)-avr(x,30))^2;
b:=b1/b2;
a:=avr(y,30)-b*avr(x,30);
SLOPE=(X,N)
It means that the line is estimated by the least square method of the sample line with n values, and the slope is the previous B