Question

point of intersection for y=2x+2 and y=-2/3x-2

Answer 1

To find the point of intersection between the two lines, we need to set their equations equal to each other:

2x + 2 = -2/3x - 2

First, let's get rid of the fractions by multiplying both sides of the equation by 3:

3(2x + 2) = 3(-2/3x - 2)
6x + 6 = -2x - 6

Next, let's isolate the variable x:

6x + 6 = -2x - 6
Add 2x to both sides:
6x + 2x + 6 = -2x - 6 + 2x
8x + 6 = -6
Subtract 6 from both sides:
8x = -12
Divide by 8:
x = -12/8
x = -3/2

Now that we have the x-value, we can substitute it back into one of the original equations to solve for y. Let's use y = 2x + 2:

y = 2(-3/2) + 2
y = -3 + 2
y = -1

Therefore, the point of intersection between the two lines is (-3/2, -1).