Question

using a linear model, which equation best models the set of data in the table below?
1 7
3 10
5 16
7 19
9 24
y = 1.5x + 5.5
y = 2.15x + 4.45
y = -2.15x + 4.45
y = 2.15x + 7

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(1,7)\) and \((x_2,y_2)=(3,10)\).
\(m=\frac{10 - 7}{3 - 1}=\frac{3}{2}=1.5\).
Let's check with another pair \((x_1,y_1)=(5,16)\) and \((x_2,y_2)=(7,19)\).
\(m=\frac{19 - 16}{7 - 5}=\frac{3}{2}=1.5\).

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((1,7)\) and \(m = 1.5\), \(y-7=1.5(x - 1)\).
Expand: \(y-7=1.5x-1.5\).
Then \(y=1.5x+5.5\).

Answer:

\(y = 1.5x+5.5\)