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Ainat [17]
3 years ago
8

Determine the intercepts of the line that correspond to the following table of values

Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
3 0

Answer:

x-intercept:  (-21,0); y-intercept:  (0, 14)

Step-by-step explanation:

Let's first look at changes in x.  x begins at -24 and increases by 9 to -15.  At the same time, y begins at -2 and decreases to -8.  Thus, the slope of the line in question is m = rise / run = -6/9 = -2/3.

Let's find the equation of the line in the simplest way:  point-slope form.

y-(-2) = (-2/3)(x-[-24]).  Then y+2 = (-2/3)x - (2/3)(24)), or

                                              y + 2 = - (2/3)x + 16.

<u>x-intercept</u>:  Let y = 0 and find x:  0 + 2 = -(2/3)x + 16, or 0 = -(2/3)x + 14.

Multiplying all terms by (-3/2), we get 0 =  -x + 14(-3/2), or x = -21.  Then the x-intercept is (-21, 0).

y-intercept:  let x = 0 and find y:    y + 2 = -(2/3)(0) + 16.  Then y = 14.  The y-intercept is (0, 14).


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Solve for x.<br> 7(1x - 3) = 4(x + 5)
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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

7(1x - 3) = 4(x + 5)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Simplify:                                        7(x - 3) = 4(x + 5)
  2. Distribute:                                     7x - 21 = 4x + 20
  3. Subtract 4x on both sides:          3x - 21 = 20
  4. Add 21 on both sides:                  3x = 41
  5. Divide 3 on both sides:                x = 41/3

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    7(1(41/3) - 3) = 4(41/3 + 5)
  2. Multiply:                        7(41/3 - 3) = 4(41/3 + 5)
  3. Subtract/Add:               7(32/3) = 4(56/3)
  4. Multiply:                        224/3 = 224/3

Here, we see that 224/3 is indeed equivalent to 224/3. ∴ x = 41/3 is a solution to the equation.

And we have our final answer!

6 0
2 years ago
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