Question

Can someone help? Find the intersection of the line through the points (7,6) and (4,2) with the line y=x . The point of intersection is (A,B) . What is the value of A and B?

Answer 1

can you find the equation of line through the points (7,6) and (4,2) ?

Answer 2

first you need to find slope ,
The slope of the line through points (x1,y1) and (x2,y2) is given by :
\(\huge m=\frac{y_1-y_2}{x_1-x_2}\)
now,just put the values and find m.

Answer 3

m=4/3 right?

Answer 4

absolutely!
now equation of line will be
y-y1 = m (x-x1)
you can use any of the 2 points for x1,y1.

Answer 5

can u find equation of line ? or need help with that ?

Answer 6

y=4/3x-2 2/3 is that right?

Answer 7

y-2=4/3(x-4) that is what I had at first.

Answer 8

thats correct, to find the intersection point you need to solve both equations simultaneously,
that is put x=y in y-2=4/3(x-4)
and find the value of x (or y)

Answer 9

then x=y=A=B

Answer 10

A=10
B=10