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The point-slope form of the equation of the line that passes through [tex]$(-9,-2)$[/tex] and [tex]$(1,3)$[/tex] is [tex]$y - 3 = \frac{1}{2}(x - 1)$[/tex]. What is the slope-intercept form of the equation for this line?

A. [tex]$y = \frac{1}{2} x + 2$[/tex]
B. [tex][tex]$y = \frac{1}{2} x - 4$[/tex][/tex]
C. [tex]$y = \frac{1}{2} x + \frac{5}{2}$[/tex]
D. [tex]$y = \frac{1}{2} x - \frac{7}{2}$[/tex]

Sagot :

GinnyAnswer
To convert the given point-slope form equation to slope-intercept form, follow these steps:

### Given Equation:
[tex]\[ y - 3 = \frac{1}{2}(x - 1) \][/tex]

### Step-by-Step Solution:

1. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the right side:
[tex]\[ y - 3 = \frac{1}{2}x - \frac{1}{2} \][/tex]

2. Isolate [tex]\(y\)[/tex] by adding 3 to both sides of the equation:
[tex]\[ y = \frac{1}{2}x - \frac{1}{2} + 3 \][/tex]

3. Combine the constants on the right side:
[tex]\[ y = \frac{1}{2}x + \left(3 - \frac{1}{2}\right) \][/tex]
[tex]\[ y = \frac{1}{2}x + \frac{6}{2} - \frac{1}{2} \][/tex]
[tex]\[ y = \frac{1}{2}x + \frac{5}{2} \][/tex]

Thus, the slope-intercept form of the equation is:
[tex]\[ y = \frac{1}{2}x + \frac{5}{2} \][/tex]

The correct answer is:
[tex]\[ \boxed{y = \frac{1}{2}x + \frac{5}{2}} \][/tex]
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