Question

A graph of an additive pattern contains the points (3,16)
and (8,21)
. What expression does the graph represent?(1 point)
x+

Answer 1

To find the expression that represents the additive pattern described by the points (3, 16) and (8, 21), we first need to determine the change in y (the output) as we change x (the input) between these two points.

1. **Identify the coordinates:**
- First point: (3, 16) → x₁ = 3, y₁ = 16
- Second point: (8, 21) → x₂ = 8, y₂ = 21

2. **Calculate the change in x and y:**
- Change in x (Δx) = x₂ - x₁ = 8 - 3 = 5
- Change in y (Δy) = y₂ - y₁ = 21 - 16 = 5

3. **Determine the additive pattern:**
The change in y is constant (5) for a change of 5 in x, which indicates a linear relationship with a slope of 1.

4. **Find the linear expression:**
We can express this pattern in the form \(y = mx + b\) where m is the slope and b is the y-intercept.

Given that:
- Slope \(m = \frac{Δy}{Δx} = 1\)

Using the point (3, 16) to find the y-intercept (b):
\[
16 = 1(3) + b
\]
\[
16 = 3 + b
\]
\[
b = 16 - 3 = 13
\]

5. **Write the expression:**
The equation representing the pattern is:
\[
y = 1x + 13
\]
or simply:
\[
y = x + 13
\]

Therefore, the expression that represents the graph is:

**x + 13**.