Question

Which of the following formulas can represent the points (1,2),(2,6),(3,10),(4,14) ?(1 point) Responses y=−4x+2 y is equal to negative 4 x plus 2 y=4x+2 y is equal to 4 x plus 2 y=4x−2 y is equal to 4 x minus 2 y=−4x−2

Answer 1

To determine which formula can represent the points (1,2), (2,6), (3,10), and (4,14), we can analyze the points and check for a linear relationship.

We can first calculate the differences in y-values and corresponding x-values:

1. From (1, 2) to (2, 6):
- Change in y = 6 - 2 = 4
- Change in x = 2 - 1 = 1

2. From (2, 6) to (3, 10):
- Change in y = 10 - 6 = 4
- Change in x = 3 - 2 = 1

3. From (3, 10) to (4, 14):
- Change in y = 14 - 10 = 4
- Change in x = 4 - 3 = 1

The change in y is consistently 4 for each change in x of 1, indicating a linear relationship with a slope of 4.

Thus, the slope (m) is 4. We can use the slope-intercept form of a linear equation, \(y = mx + b\), where \(m = 4\).

Now we can substitute one of the points to find the y-intercept (b). We'll use the first point (1, 2):

\[
2 = 4(1) + b
\]
\[
2 = 4 + b
\]
\[
b = 2 - 4 = -2
\]

So the equation of the line is:

\[
y = 4x - 2
\]

This corresponds to the response:

**y = 4x - 2**.

Thus, the correct formula that represents the points is \( y = 4x - 2 \).