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 minus 3

y=−2x+3
y equals negative 2 x plus 3

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

y=2x−3
y equals 2 x minus 3

Answer 1

To find the formula for the points (1,5), (2,7), (3,9), and (4,11), we can observe the pattern in the y-values corresponding to the x-values.

Let's look at the given points:

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

We can see that as \( x \) increases by 1, \( y \) increases by 2. This indicates a linear relationship with a slope of 2.

Now, using the point-slope form of a linear equation, we can express this:

- The slope (m) = 2
- We can use any point to find the y-intercept (b). Using the point (1, 5):

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

So, the equation of the line in slope-intercept form is:

\[ y = 2x + 3 \]

Thus, the correct answer from the provided options is:

**y = 2x + 3**.