Question

Describe the pattern in the table using words, an equation and a graph. Extend the pattern for x=5,6,7.

Table
X Y
1 15
2 25
3 35
4 45

Answer 1

The graph would be y = 10x + 5 and the values for 5, 6 and 7 would be as follows (5, 55), (6, 65), and (7, 75).

In order to find this, first find the slope of the equation. You can do this by using the slope formula with any points given.

m (slope) = (y2 - y1)/(x2 - x1)

In this equation (x1, y1) is the first point and (x2, y2) is the second. We'll use (1, 15) and (2, 25) as our points.

m = (y2 - y1)/(x2 - x1)

m = (25 - 15)/(2 - 1)

m = 10/1

m = 10

Now that we have the slope, we can use a point and the slope to find the y-intercept.

y = mx + b

15 = 10(1) + b

15 = 10 + b

5 = b

Now we put that all together to complete the model.

y = 10x + 5

And we can use that formula to solve for x = 5, 6 and 7.