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

Answer: 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).

## Related Questions

David borrowed \$2500 from his local bank. The yearly interest rate is 8%. If David pays the full principle and interest in the first year of the loan, how much money will he pay to the bank?

Step-by-step explanation: Really depends on the kind of interest, but you would take the initial amount, and multiply it by the APR for the amount of interest, then add the interest to the initial amount.

The following are the ages (years) of 5 people in a room: 23, 13, 17, 12, 15 A person enters the room. The mean age of the 6 people is now 22. What is the age of the person who entered the room?

23 because they are all 23 put together

Rewrite the following parametric equations in rectangular form.

x=e^3t
y=e^-t

To solve this problem you must apply the proccedure shown below:
1. You have the following parametric equations given in the problem above:
x=e^3t
y=e^-t
2. Therefore, you must solve fot et in the second equation, as below:
y=e^-t
y=1/e^t
e^t=1/y
3.Substitute into the first equation:
x=e^3t
x=(e^t)^3
x=(1/y)^3
x=1/y^3   (y>0)