Question

Are the lines described by the equations y=x+2 and x+y=6 intersecting, coinciding, or parallel? Explain

Answer 1

y = slope*x + y-intercept;
We can rewrite our equation in a shorter form : y = mx + b;
y = x + 2 ; m1 = 2 and b1 = 2;
y = -x + 6; m2 = -1 and b2 = 6;
Set the two equations for y equal to each other:
x + 2 = -x + 6 ;
Solve for x. This will be the x-coordinate for the point of intersection:
2x = 4;
x = 2;
Use this x-coordinate and plug it into either of the original equations for the lines and solve for y. This will be the y-coordinate of the point of intersection:
y = 2 + 2 ;
y = 4;
The point of intersection for these two lines is (2 , 4).