Question

Equation of the Line

Answer 1

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Answer:

  a) (0, 5/2), (5/3, 0)

  b) m = -3/2; b = 5/2

  c) (5/3, 0), (0, 5/2)

Step-by-step explanation:

Given:

  3x +2y = 5

Find:

  a) two points that satisfy the equation

  b) slope and y-intercept

  c) x-intercept

Solution:

Since the intercepts are points on the line, finding them satisfies all parts of the question except finding the slope.

a) Let x=0. Then we can find y from ...

  3·0 +2y = 5

  y = 5/2

One point is (0, 5/2).

Let y=0. Then we can find x from ...

  3x +2·0 = 5

  x = 5/3

Another point is (5/3, 0).

Two points on the line are (0, 5/2) and (5/3, 0).

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b) The slope can be found using the slope formula on the two points we found.

  m = (y2 -y1)/(x2 -x1)

  m = (0 -5/2)/(5/3 -0) = -(5/2)/(5/3) = -3/2

The slope is -3/2. The y-intercept is 5/2.

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c) The x- and y-intercepts are (5/3, 0) and (0, 5/2), respectively.