Question

Find the distance between the x-intercept and the y-intercept of the graph of the equation 5x - 12y = 60.

Answer 1

`d = 13`

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:
  `d = √((x_2-x_1)^2+(y_2-y_1)^2)`

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:
   `d = √((0-12)^2+(-5-0)^2)`
2. Subtract:
   `d = √((-12)^2+(-5)^2)`
3. Evaluate:
   `d = √(144+25)`
4. Add:
   `d = √(169)`
5. Evaluate:
   `d = 13`