Question

Create a formula for the points (1,5),(2,7(,(3,9), and (4,11)
y =2x-3
y =-2x+3
y=2x+3
y =-2x-3

Answer 1

To determine the correct formula for the points (1,5), (2,7), (3,9), and (4,11), we need to identify the linear equation that passes through these points.

1. We can observe the \(y\)-values:
- For \(x = 1\), \(y = 5\)
- For \(x = 2\), \(y = 7\)
- For \(x = 3\), \(y = 9\)
- For \(x = 4\), \(y = 11\)

2. The \(y\)-values appear to increase by 2 for every increase of 1 in the \(x\)-values. This indicates a slope of 2.

3. The equation of a line can be expressed in the slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

4. Using the slope \(m = 2\), we can substitute one of the points to find \(b\). Let's use the point \((1, 5)\):

\[
5 = 2(1) + b
\]
\[
5 = 2 + b
\]
\[
b = 5 - 2 = 3
\]

5. Therefore, the equation of the line fitting the points is:

\[
y = 2x + 3
\]

This matches one of the options you provided: **y = 2x + 3**.