Each triangle has a side length of 1, which is why the perimeter of the single triangle is 3. We just add up the three sides (1+1+1 = 3).
Similarly, the perimeter of the second figure is 4 because we have 4 sides that are same length which add up to 4 total (1+1+1+1 = 4).
Pattern #3 has a perimeter of 5 because the bottom length is 2 units long, the top length is 1 unit long, and each diagonal is 1 unit long. So we have 5 total.
The perimeters so far are: 3, 4, 5
Each time we are adding 1 to the old perimeter to get the new perimeter. So pattern #4 will have a perimeter of 6. Sure enough, if you count the sides out, then you should get 6 total.
Note: only count out the exterior sides. Do not count the interior sides.
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x = number of triangles, y = perimeter
If x = 1, then y = 3
If x = 2, then y = 4
if x = 3, then y = 5
If x = 4, then y = 6
Whatever x is, we add on 2 to get the value of y.
So the equation is therefore y = x+2. If you want, you can use the slope formula to find the value of m. Then use it to find the value of b, so you determine that y = mx+b turns into y = 1x+2 which is the same as y = x+2
Answer: y = x+2