There are more than a half-dozen different forms of the equation for a line. They are useful for different purposes. One of them is the "two-point form".

Using x as the independent variable, and y as the dependent variable, the equation can be written as ...

y -y1 = (y2 -y1)/(x2 -x1)/(x -x1)

where (x1, y1) and (x2, y2) are the two points.

Here, your two points are ...

(t, s) = (10, 337) and (30, 349)

Using s in place of y, and t in place of x, these two points go into the formula like this:

s -337 = (349 -337)/(30 -10)(t -10)

Simplifying the fraction, this is ...

s -337 = (12/20)(t -10)

And writing it as a decimal, we get ...

s -337 = 0.6(t -10)

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<em>Additional comments</em>

Adding y1 to both sides of the above form gives you ...

y = (y2 -y1)/(x2 -x1)/(x -x1) +y1

This is the form I usually prefer to use, because it can lead directly to slope-intercept form. For this problem, the form shown above gets you to the answer you're looking for.

This "two-point form" is an expansion of the "point-slope form", which is ...

y - k = m(x -h) . . . . . . . line with slope m through point (h, k)

where the equation for slope is ...

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

and (x1, y1) is used instead of (h, k).

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3 years ago

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