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stealth61 [152]
4 years ago
10

Determine whether y varies directly with x. Find the constant of variation. Write the function rule x 5 7 9 y 6 11 16

Mathematics
1 answer:
daser333 [38]4 years ago
4 0

Answer:

  a)  y does NOT vary directly with x

  b)  y = 2.5x -6.5

Step-by-step explanation:

If variation were direct the ratios of y to x would be constant. They are not:

  6/5 ≠ 11/7

y does not vary directly with x.

__

y changes by 5 from 6 to 11 when x changes by 2 from 5 to 7. Then the slope of the linear function rule is (change in y)/(change in x) = 5/2. Using a point-slope form of the equation of a line, we can write the rule as ...

  y = m(x -h) +k . . . . . . . . for a line of slope m through point (h, k)

  y = (5/2)(x -5) +6

  y = 2.5x -6.5 . . . . . simplify

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ivolga24 [154]

<u>Answer:</u>

<h2>A = 15 u²</h2>

<u>Explanation:</u>

according to the coordinates the triangles is right at the pair (2, -3)

the area of the triangle = height × base × 1/2

the <u>height</u> is the line passing through the pairs (-1, 6) and (2, -3)

h² = (2-(-1))²+(-3-6)²

h² = 3² + (-9)²

h² = 9 + 81

h² = 90

h = √90

the <u>base</u> is the line passing through the pairs (5, -2) and (2, -3)

b² = (2-5)²+(-3-(-2))²

b² = 3² + (-3+2)²

b² = 9 + 1

b² = 10

b = √10

A = h×b×1/2

A = √90×√10×1/2

A = √900×1/2

A = 30×1/2

A = 15 u²

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