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y = (1/4)x + 37

Step-by-step explanation:

Determine the equation of the line through (76, 56) and (212, 90).

As we move from (76, 56) to (212, 90), x increases by 136 and y by 34.

Thus, the slope of this line is m = 34/ 136, or 0.25, or 1/4.

Let's subst. some of this "known" info into the point-slope equation of a straight line, which is y - k = m(x - h):

y - 90 = (1/4)(x - 212)   (which is the data from (212, 90).

We must solve this for y and then simplify the resulting equation:

Adding 90 to both sides, we get:

y = (1/4)(x - 212) + 90, which works out to:

y = (1/4)x - 53 + 90, or

y = (1/4)x + 37

What does this mean?  x represents the outside temperature and y the number of cricket chirps.

If the outside temp. is 0 (that is, if x = 0), then y = 0 + 37, or y = 37.  This is the y-intercept of the line.

For each degree that the temperature rises, the number of chirps increases by 1/4.  A better way to put this is to say, for each 4 degrees that the temp rises, the number of chirps increases by 1.

b

step-by-step explanation: