Question

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

y=2x−3
𝑦
=
2
𝑥
−
3
y equals 2 x minus 3

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

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

y=−2x−3

Answer 1

To find the correct formula for the points (1, 5), (2, 7), (3, 9), and (4, 11), we can first observe the relationship between the x-values and y-values.

The points can be summarized as follows:
- For x = 1, y = 5
- For x = 2, y = 7
- For x = 3, y = 9
- For x = 4, y = 11

We can see a pattern that for each increase of 1 in x, y increases by 2. This suggests a linear relationship of the form:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

1. **Calculate the slope (m)**:
\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{7-5}{2-1} = 2
\]

2. **Use one of the points to solve for b**:
Using the point (1, 5):
\[
5 = 2(1) + b
\]
\[
5 = 2 + b
\]
\[
b = 3
\]

Putting it all together, the formula is:
\[
y = 2x + 3
\]

Therefore, the correct response is:
**y = 2x + 3**.