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Select the equation for the line in point-slope form.

Select the equation for the line in point-slope form.-example-1
User CREcker
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1 Answer

6 votes

Answer:

(d) y -8 = -5/8(x +8)

Explanation:

You want the point-slope equation for the line through the points listed in the table.

Point-slope form

The point-slope form of the equation for a line is ...

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

Application

The first point listed in the table is (h, k) = (-8, 8), so the equation will be of the form ...

y -8 = m(x -(-8))

y -8 = m(x +8)

Comparing this form to the answer choices, we see that it matches choices (b) and (d). These have m = -8/5 and m = -5/8, respectively.

Slope

The slope of the line is given by the formula ...

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

m = (4 7/8 -8)/(-3 -(-8)) = (-3 1/8)/5

Clearly the magnitude of this is less than 1, so cannot match m=-8/5, which has a magnitude greater than 1. The appropriate answer choice is (d):


\boxed{y-8=-(5)/(8)(x +8)}

__

Additional comments

The slope can be worked out to be ...

(-3 1/8)/5 = (-25/8)/5 = -5/8

This confirms our answer choice.

We know the magnitude of (-3 1/8)/5 is less than 1 because 3 1/8 < 5.

User LookIntoEast
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