1. Calculate the equation of the line through the points (1, 1), (4, 3), (10, 7) and (40, 27).

y = (2/3)x + 1/3

Step-by-step explanation:

Check that a single straight line will actually go through all four of these points.  Going from (1, 1) to (4, 3), the 'rise' is 2 and the 'run' is 3, which would make the slope, m, equal rise/run = 2/3.  Going from (4,3) to (10, 7), m = rise/run = 4/6 = 2/3 (again).

Let's find the slope-intercept form of the equation of this line:  y = mx + b

Arbitrarily choose the point (1, 1).  Here x = 1, y = 1 and m = 2/3.  Then

we have

1 = (2/3)(1) + b, or 1 = 2/3 + b, so that b must be 1/3.

The equation in question is y = (2/3)x + 1/3

step-by-step explanation:

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