Question

1. the graph of which of the following equations has a slope of -\frac{1}{2} and an x - intercept of (-6,0)?
2. y = -\frac{1}{2}x - 6
3. y = -\frac{1}{2}x + 3
4. y = -\frac{1}{2}x + 6
5. y = -\frac{1}{2}x - 3

Explanation:

Step1: Use slope-intercept form

The line equation is \( y = mx + b \), where \( m = -\frac{1}{2} \) (slope).

Step2: Find x-intercept condition

x-intercept \((-6,0)\) means \( y=0 \) when \( x=-6 \). Substitute into \( 0 = -\frac{1}{2}(-6) + b \).

Step3: Solve for b

\( 0 = 3 + b \Rightarrow b = -3 \). Thus, equation: \( y = -\frac{1}{2}x - 3 \).

Answer:

D. \( y = -\frac{1}{2}x - 3 \)