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

Answer 1

We can start by finding the slope of the line passing through any two points and then use the slope and one point to find the equation of the line. Once we have the equation of the line, we can substitute the x-coordinate of the remaining points to find their corresponding y-coordinates.

Using the points (1,5) and (2,7) to find the slope:

m = (y2 - y1) / (x2 - x1)
m = (7 - 5) / (2 - 1)
m = 2 / 1
m = 2

Now, we use the point (1,5) and the slope m = 2 to find the equation of the line:

y - y1 = m(x - x1)
y - 5 = 2(x - 1)
y - 5 = 2x - 2
y = 2x + 3

Now that we have the equation of the line, we can substitute the x-coordinates of the remaining points to find their corresponding y-coordinates:

For x = 3:
y = 2(3) + 3
y = 6 + 3
y = 9

So, the point (3,9) is on the line.

For x = 4:
y = 2(4) + 3
y = 8 + 3
y = 11

So, the point (4,11) is also on the line.

Therefore, the formula for the points (1,5), (2,7), (3,9), and (4,11) is y = 2x + 3.