Question

Create a formula for the points (1,5) , (2,7) , (3,9) , and (4,11) .(1 point)
Responses

y=−2x+3
y equals negative 2 x plus 3

y=−2x−3
y equals negative 2 x minus 3

y=2x−3
y equals 2 x minus 3

y=2x+3
y equals 2 x plus 3

Answer 1

To find the formula that represents the points (1,5), (2,7), (3,9), and (4,11), we can start by observing the relationship between the x and y coordinates.

Let's identify the pattern:

1. When \( x = 1 \), \( y = 5 \).
2. When \( x = 2 \), \( y = 7 \).
3. When \( x = 3 \), \( y = 9 \).
4. When \( x = 4 \), \( y = 11 \).

To find the slope \( m \) of the line, we can use two points. For example, taking points (1,5) and (2,7):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2
\]

The slope is 2. Now we can use point-slope form \( y - y_1 = m(x - x_1) \) to find the equation of the line. Using point (1,5):

\[
y - 5 = 2(x - 1)
\]

Simplifying this gives us:

\[
y - 5 = 2x - 2
\]
\[
y = 2x + 3
\]

Thus, the equation that fits all the points is:

\[
y = 2x + 3
\]

Therefore, the correct response is:

**y = 2x + 3**.