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Ivahew [28]
2 years ago
13

Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (5, 2), (3, 3)

Mathematics
2 answers:
Strike441 [17]2 years ago
8 0

Answer:

-0.5

Step-by-step explanation:

  • slope=rise/run or y/x in other words(y2-y1/x2-x1)
  • (y2-y1) is 3-2 so y2-y1=1
  • (x2-x1) is 3-5 so x2-x1= -2
  • -1/2 or -0.5 would be the slope.
Sindrei [870]2 years ago
8 0

Answer:

1/-2

Step-by-step explanation:

5 = x1, 2 = y1

3 = x2, 3 = y2

y is always before x

y2 - y1 = 3 - 2

3 - 2 = 1

You can always subtract y1 by y2, but I am just doing it the other way. But if you choose to subtract 2 by 1, you have t do that for x also.

x2 - x1 = 3 - 5

3 - 5 = -2

After this step, you put y on top, and x on the bottom, making:

1/-2

:)

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Given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and \frac{(f(a + h) - f(a)) }{h} by substituting their values into f(x) = 3x + 6. We will have the following:

\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}

<em><u>Given:</u></em>

  • f(x) = 3x + 6

<em>We are told to find:</em>

  1. f(a)
  2. f(a + h), and
  3. \frac{(f(a + h) - f(a)) }{h}

1. <em><u>Find f(a):</u></em>

  • Substitute x = a into f(x) = 3x + 6

f(a) = 3(a) + 6

f(a) = 3a + 6

<em>2. Find f(a + h):</em>

  • Substitute x = a + h into f(x) = 3x + 6

f(a + h) = 3(a + h) + 6

f(a + h) = 3a + 3h + 6

<em>3. Find </em>\frac{(f(a + h) - f(a)) }{h}<em>:</em>

  • Plug in the values of f(a + h) and f(a) into \frac{(f(a + h) - f(a)) }{h}

Thus:

\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\

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\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}

Therefore, given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and \frac{(f(a + h) - f(a)) }{h} by substituting their values into f(x) = 3x + 6. We will have the following:

\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}

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astra-53 [7]

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