Question

Write a linear equation in the form of y = mx + b for the following table. Click Here for Help Video



𝑥
x
𝑦
y
2
2
8
8
4
4
15
15
6
6
22
22



𝑦
=
y=

𝑥
x
+
+

Answer 1

To write a linear equation in the form \( y = mx + b \), we need to identify the slope \( m \) and the y-intercept \( b \) from the provided data points.

Given the points from the table:
- (2, 8)
- (4, 15)
- (6, 22)

### Step 1: Calculate the slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the first two points (2, 8) and (4, 15):
\[
m = \frac{15 - 8}{4 - 2} = \frac{7}{2} = 3.5
\]

### Step 2: Find the y-intercept \( b \)
We can use one of the points and the slope to find the y-intercept \( b \). We can use the point (2, 8):
\[
y = mx + b
\]
Substituting the values:
\[
8 = 3.5(2) + b
\]
\[
8 = 7 + b
\]
\[
b = 8 - 7 = 1
\]

### Step 3: Write the equation
Now, substituting \( m \) and \( b \) back into the linear equation format:
\[
y = 3.5x + 1
\]

Therefore, the equation that represents the relationship between \( x \) and \( y \) in the given table is:
\[
y = 3.5x + 1
\]