Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Writing a Linear Equation in Slope-Intercept Form**

**Objective:** Learn how to write the equation of a line using the slope-intercept form.

**Problem Statement:**

Write an equation in slope-intercept form for the line that has a slope of \( \frac{2}{3} \) and a y-intercept of (0, -5).

**Solution:**

To find the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:

1. Identify the slope \( m = \frac{2}{3} \).
2. Identify the y-intercept \( b = -5 \).

**Equation:**

\[ y = \frac{2}{3}x - 5 \]

**Check Understanding:**

Now, use the point-slope form template to verify:
\[
\text{Point Slope form: }\ y - \_ = \frac{2}{3}(x - \_)
\]

Fill with given values:
- The y-intercept point is (0, -5), so the formula becomes:
  \[
  y + 5 = \frac{2}{3}(x - 0)
  \]

This aligns with the slope-intercept form determined above.
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Transcribed Image Text:**Writing a Linear Equation in Slope-Intercept Form** **Objective:** Learn how to write the equation of a line using the slope-intercept form. **Problem Statement:** Write an equation in slope-intercept form for the line that has a slope of \( \frac{2}{3} \) and a y-intercept of (0, -5). **Solution:** To find the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept: 1. Identify the slope \( m = \frac{2}{3} \). 2. Identify the y-intercept \( b = -5 \). **Equation:** \[ y = \frac{2}{3}x - 5 \] **Check Understanding:** Now, use the point-slope form template to verify: \[ \text{Point Slope form: }\ y - \_ = \frac{2}{3}(x - \_) \] Fill with given values: - The y-intercept point is (0, -5), so the formula becomes: \[ y + 5 = \frac{2}{3}(x - 0) \] This aligns with the slope-intercept form determined above.
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