Question

write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation. f(x) = 2x 12 f(x) = 6x − 12 y = 2x 12 y = 6x − 12

Answer 1

f(x) = (1/6)x + 11/2.

Explanation:

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Answer 2

Explanation:

As we move from (3, 6) to (5, 18), x increases by 2 (this is the "run") and y increases by 12 (this is the "rise").

Thus, the slope of this line is m = rise / run = 12 / 2, or m = 1/6.

Apply the slope-intercept form of the equation of a straight line:

y = mx + b becomes 6 = (1/6)(3) + b after substituting the coordinates 3 and 6. Then 6 = 1/2 + b, or 5 1/2 = b.

Then the equation of this line is y = (1/6)x + 11/2.

In functional notation, that would be f(x) = (1/6)x + 11/2.