Question

Write the equation of a line that passes a given point and has the given slope. Answer in standard form. 1. Point (-3,5), m = -7 2. Point (4,7), m = 0

Answer 1

1. y -5 = -7(x +3)
2. y = 7

Explanation:

The point-slope form of the equation can be used for this. It is generally written as ...

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

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1. For m=-7, (h, k) = (-3, 5), the equation is ...

y -5 = -7(x +3)

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2. For m=0, (h, k) = (4, 7), the equation is ...

y -7 = 0(x -4)

y = 7

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Comment on the form of the answer

Since a point and slope are given, "the equation" is appropriately written in point-slope form. For the second problem the simplified version would be ...

y -7 = 0

Sometimes, "the equation" means the answer is expected in slope-intercept form. In that case, a little rearranging is necessary for the first answer. It becomes ...

y = -7x -16

There are perhaps a dozen different forms that a linear equation can be written in. Considering those, "the equation" is somewhat ambiguous. Your curriculum materials may offer a clue as to the form intended.