Create a formula for the points (1,5)

Question

, (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

Answer 1

To find the correct formula that fits the points (1,5), (2,7), (3,9), and (4,11), we can first recognize that the points suggest a linear relationship because they all fall along a straight line.

Let's determine the slope (m) using two of the points, say (1, 5) and (2, 7):

1. Calculate the difference in y-values divided by the difference in x-values: \[ m = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2 \]

Now that we have the slope (m = 2), we can use the point-slope form of the linear equation to find the formula. We use the point (1, 5) to do that:

2. The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] Plugging in \(m = 2\), \(x_1 = 1\), and \(y_1 = 5\): \[ y - 5 = 2(x - 1) \]

3. Simplify the equation: \[ y - 5 = 2x - 2 \] \[ y = 2x + 3 \]

Thus, the equation that fits the points is:

y = 2x + 3.

The correct response is:

y = 2x + 3.