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Answer:

[tex]d = 13[/tex]

General Formulas and Concepts:

Pre-Algebra

  • Order of Operations: BPEMDAS
  • Equality Properties

Algebra I

Slope-Intercept Form: y = mx + b

  • m - slope
  • b - y-intercept

The y-intercept is the y value when x = 0.  Another way to reword that is when the graph crosses the y-axis.

The x-intercept is the x value when y = 0.  Another way to reword that is when the graph crosses the x-axis.

Algebra II

  • Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Equation 5x - 12y = 60

Step 2: Rewrite in slope-intercept form

  1. Isolate y term:                   -12y = 60 - 5x
  2. Isolate y:                            y = -5 + 5/12x
  3. Rewrite:                             y = 5/12x - 5

Step 3: Find x and y intercept

x-intercept

  1. Set y = 0:                    0 = 5/12x - 5
  2. Isolate x term:            5 = 5/12x
  3. Isolate x:                     12 = x
  4. Rewrite:                      x = 12

y-intercept

  1. Define:                    y = 5/12x - 5
  2. Break:                     y = -5

Step 4: Write coordinates

x-int (12, 0)

y-int (0, -5)

Step 5: Find distance d

  1. Substitute:                    [tex]d = \sqrt{(0-12)^2+(-5-0)^2}[/tex]
  2. Subtract:                       [tex]d = \sqrt{(-12)^2+(-5)^2}[/tex]
  3. Evaluate:                       [tex]d = \sqrt{144+25}[/tex]
  4. Add:                              [tex]d = \sqrt{169}[/tex]
  5. Evaluate:                      [tex]d = 13[/tex]

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