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yanalaym [24]
3 years ago
5

What is the equation of the line that passes through (5,-2) and (-3,4)

Mathematics
1 answer:
Gennadij [26K]3 years ago
3 0

Answer:

3x + 4y = 7

Step-by-step explanation:

The slope = difference of y values / corresponding difference in x values of the 2 points.

Here it  is (4 - (-2) / (-3 - 5)

= 6 /-8 = -3/4.

Now we use the point/slope form of the equation of a line:

y - y1 = m(x - x1)  where m = slope and (x1, y1) is a point on the line.

We take the point (5, -2) and m = -3/4:

y - (-2) = -3/4 (x - 5)

y + 2 = -3/4x + 15/4

y = -3/4 x + 15/4 - 8/4

y = -3/4 x + 7/4  This is the equation in slope/intercept form.

To convert it to standard form we multiply through by 4 and rearrange:

4y = -3x + 7

3x + 4y = 7  is standard form.

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Step-by-step explanation:

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Determine the area of the coin to the nearest tenth.
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What is the solution to the pair of simultaneous equations? 2x+y=5. 3x-2y=4​
densk [106]

Answer:

(2, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Distributive Property

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)
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Step-by-step explanation:

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

2x + y = 5

3x - 2y = 4

<u>Step 2: Rewrite Systems</u>

<em>Manipulate 1st equation</em>

  1. [Subtraction Property of Equality] Subtract 2x on both sides:                      y = 5 - 2x

<u>Step 3: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em> [2nd Equation]:                                                                         3x - 2(5 - 2x) = 4
  2. [Distributive Property] Distribute -2:                                                                3x - 10 + 4x = 4
  3. [Addition] Combine like terms:                                                                        7x - 10 = 4
  4. [Addition Property of Equality] Add 10 on both sides:                                   7x = 14
  5. [Division Property of Equality] Divide 7 on both sides:                                 x = 2

<u>Step 4: Solve for </u><em><u>y</u></em>

  1. Substitute in <em>x</em> [Modified 1st Equation]:                                                           y = 5 - 2(2)
  2. Multiply:                                                                                                             y = 5 - 4
  3. Subtract:                                                                                                            y = 1
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Answer:

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Substitute x=15 and y=3 into the equation given.

Transpose so that r = 3/15

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