4-6.) Find the x- 4. 4x - 7y = 28 10150 500

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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Find the x and y intercepts (written as a point)
**Finding Intercepts: Problem Example**

**Problem Instructions:**

4-6.) Find the x- and y-intercepts of the given equation.

**Example Problem:**

**4. \( 4x - 7y = 28 \)**

**Solution:**

To find the intercepts of the equation \( 4x - 7y = 28 \), follow these steps:

**1. Finding the x-intercept:**
   - To find the x-intercept, set \( y = 0 \) in the equation and solve for \( x \).
   - \( 4x - 7(0) = 28 \)
   - \( 4x = 28 \)
   - \( x = \frac{28}{4} \)
   - \( x = 7 \)

   Therefore, the x-intercept is \( (7, 0) \).

**2. Finding the y-intercept:**
   - To find the y-intercept, set \( x = 0 \) in the equation and solve for \( y \).
   - \( 4(0) - 7y = 28 \)
   - \( -7y = 28 \)
   - \( y = \frac{28}{-7} \)
   - \( y = -4 \)

   Therefore, the y-intercept is \( (0, -4) \).

**Conclusion:**
The x-intercept of the equation \( 4x - 7y = 28 \) is \( (7, 0) \), and the y-intercept is \( (0, -4) \).
Transcribed Image Text:**Finding Intercepts: Problem Example** **Problem Instructions:** 4-6.) Find the x- and y-intercepts of the given equation. **Example Problem:** **4. \( 4x - 7y = 28 \)** **Solution:** To find the intercepts of the equation \( 4x - 7y = 28 \), follow these steps: **1. Finding the x-intercept:** - To find the x-intercept, set \( y = 0 \) in the equation and solve for \( x \). - \( 4x - 7(0) = 28 \) - \( 4x = 28 \) - \( x = \frac{28}{4} \) - \( x = 7 \) Therefore, the x-intercept is \( (7, 0) \). **2. Finding the y-intercept:** - To find the y-intercept, set \( x = 0 \) in the equation and solve for \( y \). - \( 4(0) - 7y = 28 \) - \( -7y = 28 \) - \( y = \frac{28}{-7} \) - \( y = -4 \) Therefore, the y-intercept is \( (0, -4) \). **Conclusion:** The x-intercept of the equation \( 4x - 7y = 28 \) is \( (7, 0) \), and the y-intercept is \( (0, -4) \).
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