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a. Write an algorithm that determine the coefficients a and b of the equation (y = a * x + b) of a line from two points P and Q.P and Q should be entered by the user.

b. Write an algorithm that determine the point of intersection of two lines having the form y = a * x + b


so I've been stuck on it for hours would appreciate some assistant , Thank you :)
Both are very simple exercises. Can you solve them mathematically first? or your problem is implementing your solution?
programmatically i think i can manage but the math here... it's been a while since i've studied any math :/
appreciate any help
y is a polynomial function of the first degree. You can easily find a and b with 2 points using the relation a= (y(P) - y(Q))/(x(P)-x(Q) then b= y(P)-a*x(P) I'm not 100% sure about the relation regarding "a" but I remember that it was something of the sort if it's something else please correct me. This is basically the Math part, if you need any more help don't hesitate to send me a private message.
Charles.S wrotea. Write an algorithm that determine the coefficients a and b of the equation (y = a * x + b) of a line from two points P and Q.P and Q should be entered by the user.
Can you find a and b with only two variables, x an y? I don't think so. What type are P and Q anyway? coordinates (x,y)?
Charles.S wrote b. Write an algorithm that determine the point of intersection of two lines having the form y = a * x + b
I could maybe write a big procedural algorithm, but I'm not even sure.
For the first one, it's well know that 
(Y - Yp) / (X - XP) = (Yq - Yp) / (Xq - Xp)
so if you try to write the above formula in the form of y = ax + b you get the following
y = ( (Yq - Yp) / (Xq - Xp) ) * x + ( ( (Xq - Xp) * Yp + (Yp - Yq) * Xp ) / (Xq - Xp) )
Just wrote it, make sure it's correct. It involves some basic manipulation.

To calculate a and b just map them to their respective in the above equation and you get: 
a = (Yq - Yp) / (Xq - Xp)
b = ( (Xq - Xp) * Yp + (Yp - Yq) * Xp ) / (Xq - Xp)
# EDIT: just a small note, that's the generic formula I mentioned, you can easily simplify the b formula and get the following:
b = Yp - a*Xp
So if you have P (1, 2) and Q (2, 4), notice that Q coordinates are double of P, it's expected to get y = 2x where a = 2 and b = 0 which you can calculate with what's mentioned above.


For the second one, you have 2 lines which results in 2 linear equations where you have a and b obviously. If you have 2 equations with a and b given, you can find x and y easily because the interception point is where they both have the same y and x.

so if you set y1 = y2, you get a1 * x + b1 = a2 * x + b2 and you solve for x where you get something like:
(a1 - a2) * x = b2 - b1
x = (b2 - b1) / (a1 - a2)
you find x then you replace the value of x in any equation you have to calculate the value of y.
For the first question, it's Javascript, it can be run in the browser console (F12)

var X = {};
var Y = {};

['p','q'].forEach(function(p){
	var input = prompt("Enter coordinates to " + p.toUpperCase() + " as 'x,y'");
	var coords = input.split(',').map(function(s){return s.trim();});
	X[p] = coords[0];
	Y[p] = coords[1];
});

// using m0ei's work
var a = (Y.q - Y.p) / (X.q - X.p)
var b = ( (X.q - X.p) * Y.p + (Y.p - Y.q) * X.p ) / (X.q - X.p)

alert("Here are your coefficients, professor:\n a: " + a + ", b: " + b);
Not really an algorithm but meh.
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