Question

You are walking along the path y = 6x +8. Your friend is walking along the path y - 12 = 8x. At what point do your paths cross? (intersection of the two lines)

Answer 1

To find the intersection of the paths y = 6x + 8 and y - 12 = 8x, we solve the system of equations by setting them equal to each other. After solving, we discover that the paths intersect at the point (-2, -4).

Step-by-step explanation:

To determine at what point two paths intersect, we need to find the solution to the system of equations that represents these paths. Let's analyze the given equations of the paths you and your friend are walking along:

• Your path: y = 6x + 8
• Your friend's path: y - 12 = 8x or simplified to y = 8x + 12

Since both equations are equal to y, we can set them equal to each other to find the value of x where your paths cross:

6x + 8 = 8x + 12

Solving for x gives us:

6x + 8 = 8x + 12
-2x = 4
x = -2

Now, we can substitute x = -2 into either equation to find y. We'll use your path:

y = 6(-2) + 8 = -12 + 8 = -4

Therefore, the intersection point of the two paths is at the coordinates (-2, -4).